
546 N.W.2d 285 (1996)
In re ALTERNATIVE MINIMUM TAX REFUND CASES.
Nos. C2-95-1588, C5-95-1715.
Supreme Court of Minnesota.
April 12, 1996.
*287 Joe A. Walters and John Jagiela, Minneapolis, Mark S. Anderson, Minneapolis, for appellant.
Gregory P. Huwe and Barry R. Greller, Minn. Atty. Gen. Office, Tax Litigation Div., St. Paul, for respondent.
Heard, considered and decided by the court en banc.

OPINION
KEITH, Chief Justice.
On appeal from a judgment of the Ramsey County District Court, three corporations doing business in Minnesota raise state and federal constitutional challenges to a unique corporate franchise taxation scheme in effect in Minnesota between 1987 and 1989. Appellants argue that the Alternative Minimum Corporate Franchise Tax ("AMT"), embodied in Minn.Stat. §§ 290.02, 290.092 (1987), violated the Commerce Clause of the United States Constitution because it was "internally inconsistent" and discriminated against interstate commerce. Appellants also contend that the AMT created an unconstitutional classification of corporate taxpayers in violation of the Uniformity Clause of the Minnesota Constitution and the Equal Protection Clause of the United States Constitution. After a three-day trial in which appellants presented these claims, the district court rejected all of appellants' contentions and upheld the constitutionality of the AMT. Upon a successful petition by the State for accelerated review of the district court's findings, appellants renew their constitutional objections before this court. Because appellants have failed to establish that the AMT discriminated against interstate commerce or that it violated the Uniformity and Equal Protection Clauses, we affirm the district court's decision.

I.
During the mid-1980s, Minnesota had one of the highest corporate income tax rates in the United States: 12%. This tax level gave Minnesota a reputation as an "anti-business" state, which caused considerable concern among business, executive and legislative leaders. Furthermore, under the existing system approximately half of all corporations operating in Minnesota actually paid no income tax in a given year because there was no "minimum" corporate tax. Corporations that showed no taxable profits were not liable for corporate income taxes, even though they owned property in Minnesota, had Minnesota employees and sold substantial amounts of goods and services in the state. All of these factors contributed to a movement in 1987 to reform the corporate tax system in Minnesota by lowering the overall corporate income tax rate and by broadening the corporate tax base. This would permit the state to both maintain adequate tax revenue and change its high-tax "anti-business" reputation.
The new corporate minimum tax established by the legislature in 1987 is the subject of this challenge by appellants. This particular form of "alternative minimum tax" was only in effect from 1987 to 1989, and has since been replaced by a corporate alternative minimum tax based on the federal tax code. See Minn.Stat. § 290.0921 (1994).
Minnesota Statutes section 290.02 (1987) created the basic framework for the corporate franchise taxation scheme:
An annual franchise tax on the exercise of the corporate franchise to engage in contacts with this state that produce gross income attributable to sources within this state is imposed upon every corporation that so exercises its franchise during the taxable year.
* * *
The tax so imposed shall be measured by such corporations' taxable income and alternative minimum tax base for the taxable year for which the tax is imposed, and computed in the manner and at the rates provided in this chapter. *288 Id. Under this statute, a corporation's total franchise tax liability for each year was measured by the corporation's taxable income and its alternative minimum tax base. The corporate income tax was calculated at a rate of 9.5% under Minn.Stat. § 290.06, subd. 1 (1987), but only that income apportionable to Minnesota was taxed. Minn.Stat. § 290.191, subd. 1 (1987).
The AMT, however, was not based upon corporate income. It was premised upon the notion that businesses with low profits or only losses should still contribute to public finances by paying a tax proportionate to their "business activities" within the state. Thus, the AMT considered three non-income "factors" in calculating a corporation's tax base. Section 290.092 defined the alternative minimum tax base for a corporate taxpayer as the "sum of: (1) the total amount of Minnesota sales or receipts; (2) the amount of the taxpayer's total Minnesota property; and (3) the taxpayer's total Minnesota payrolls." Minn.Stat. § 290.092, subd. 3 (1987). Accordingly, the total franchise tax imposed upon corporations in Minnesota included "a tax equal to the excess, if any, of: (1) .001 multiplied by the alternative minimum tax base, over (2) the amount of tax computed under this chapter without regard to this section." Minn.Stat. § 290.092, subd. 1 (1987). This method ensured that a low profit corporation would not escape franchise taxation in Minnesota. If the corporation did not pay income tax because its profits were insufficient, it was still required to pay the AMT at a rate of .001 times its total Minnesota sales, property and payroll. And, as the district court explained, "[t]hose corporations whose franchise tax measured by taxable income, computed by multiplying 9.5% times their Minnesota taxable income, exceeded the AMT also paid the additional amount by which the franchise tax measured by taxable income exceeded the alternative minimum tax." Ultimately, corporations paid total franchise taxes equal to the greater of the factors-based AMT or the income-based 9.5% tax.
In October of 1992, a number of corporations with business operations in Minnesota filed a consolidated complaint in Ramsey County challenging the AMT on constitutional grounds and seeking a refund of excess franchise taxes paid. Each of the refund claimants paid alternative minimum taxes in excess of their regular corporate franchise income taxes between 1987 and 1989, and then unsuccessfully sought a refund of the AMT from the Minnesota Department of Revenue. Three of the original claimants, Fairway Foods, Inc., Henkel Corporation, and Juba's, Inc., were designated as representative plaintiffs for purposes of determining liability.
A three-day trial was held in Ramsey County District Court on March 1-3, 1995. Appellants presented testimony from several expert witnesses. An attorney from an accounting firm worked through the tax returns of the three representative plaintiffs, showing how the total franchise tax liability was calculated for each corporation. He also explained how a hypothetical "X Corporation" designed by appellants could pay significantly more franchise taxes under the AMT if it operated inside and outside of Minnesota than it would pay operating solely inside the state. In addition, a mathematics professor at the University of Minnesota used mathematical formulae and graphs to establish certain constitutional problems with the AMT when applied to X Corporation.[1]
*289 Following the trial, the district court rejected all of appellants' constitutional arguments and upheld the validity of the AMT. The district court found that the AMT did not impose an unlawful burden on interstate commerce, an additional tax, nor an unlawful classification of taxpayers under the state and federal constitutions. The court disagreed with appellants' contention that the tax violated the "internal consistency test" applied by the United States Supreme Court in Container Corp. v. Franchise Tax Bd., 463 U.S. 159, 169, 103 S.Ct. 2933, 2942, 77 L.Ed.2d 545 (1983), and Oklahoma Tax Comm'n v. Jefferson Lines, Inc., ___ U.S. ___, ___, 115 S.Ct. 1331, 1337, 131 L.Ed.2d 261 (1995). The court determined that appellants' use of a mathematical model and a hypothetical corporation did not establish a violation of this internal consistency principle, and corporate taxpayers in general were not exposed to a risk of multiple taxation by the AMT. Furthermore, the court found that the "credit" granted to corporations subject to the AMT for any Minnesota corporate income tax paid did not discriminate against interstate commerce by penalizing those corporations operating outside the state. Instead, this credit was simply "the arithmetic operation necessary to insure that a corporation pays the higher of the two possible franchise taxes."

II.
A determination of whether a particular state taxation scheme violates the Commerce Clause begins with the United States Supreme Court's decision in Complete Auto Transit v. Brady, 430 U.S. 274, 97 S.Ct. 1076, 51 L.Ed.2d 326 (1977). In that case, the Court set forth a four-prong test which will sustain a state tax affecting interstate commerce if: "[1] [the tax] is applied to an activity with a substantial nexus with the taxing State, [2] is fairly apportioned, [3] does not discriminate against interstate commerce, and [4] is fairly related to the services provided by the State." Id. at 279, 97 S.Ct. at 1079. Appellants' challenge to the AMT is based upon the second and third prongs of this test. Appellants have not contested the district court's conclusions that the business activities taxed are sufficiently connected to Minnesota and that the tax relates to public services provided by Minnesota, thus satisfying the first and fourth prongs of the Complete Auto standard.
The second prong, which requires a state tax to be "fairly apportioned," provides one basis for appellants' claim that the AMT is unconstitutional. Within the Commerce Clause's fair apportionment framework lies the internal consistency test relied upon by appellants and first established by the Supreme Court in Container Corp. v. Franchise Tax Bd., 463 U.S. 159, 169, 103 S.Ct. 2933, 2942, 77 L.Ed.2d 545 (1983). In Container, the Court observed that the Due Process and Commerce Clauses require each state to be fair when apportioning a corporation's income to determine how much income can be taxed by that state. Id. This fairness in apportionment of income requires both "internal" and "external" consistency in order to survive constitutional scrutiny. To be internally consistent, an apportionment formula must, "if applied by every jurisdiction, * * * result in no more than all of the unitary business' income being taxed." Id. And to be externally consistent, the same apportionment formula "must actually reflect a reasonable sense of how income is generated." Id. Thus, the requirement of fair apportionment ensures that "each State taxes only its fair share of an interstate transaction." Goldberg v. Sweet, 488 U.S. 252, 260-61, 109 S.Ct. 582, 588-89, 102 L.Ed.2d 607 (1989).
In its most recent decision under this standard, the Supreme Court explained the internal consistency mechanism:
Internal consistency is preserved when the imposition of a tax identical to the one in question by every other State would add no burden to interstate commerce that intrastate commerce would not also bear. This test asks nothing about the degree of economic reality reflected by the tax, but *290 simply looks to the structure of the tax at issue to see whether its identical application by every State in the Union would place interstate commerce at a disadvantage as compared with commerce intrastate. A failure of internal consistency shows as a matter of law that a State is attempting to take more than its fair share of taxes from the interstate transaction, since allowing such a tax in one State would place interstate commerce at the mercy of those remaining States that might impose an identical tax.
Oklahoma Tax Comm'n v. Jefferson Lines, Inc., ___ U.S. ___, ___, 115 S.Ct. 1331, 1338, 131 L.Ed.2d 261 (1995). The parties in this case agree that the internal consistency test was correctly summarized by the district court in this case. Their dispute focuses on the application of this standard to the AMT and the district court's conclusion that "[p]laintiffs' use of a mathematical model and a hypothetical corporation in an attempt to demonstrate a lack of internal consistency does not reach the level of `clear and cogent' evidence required by Container, supra, at 170, 103 S.Ct. at 2943."
Appellants' arguments at trial and on appeal rely heavily upon their mathematical proof of the alleged constitutional violations inherent in the alternative minimum tax scheme. According to appellants, once a potential variation is established between interstate and intrastate tax liability, the tax scheme violates the internal consistency test under the Commerce Clause and therefore must be struck down. The fact that X Corporation is purely hypothetical does not undermine the conclusiveness of their proof of a violation, appellants argue, since the internal consistency test itself is hypothetical in nature. As the Supreme Court has stated, the internal consistency test "asks nothing about the degree of economic reality reflected by the tax" since it requires a theoretical assumption that every state imposes the same type of tax. Jefferson Lines, ___ U.S. at ___, 115 S.Ct. at 1338. In short, appellants argue that the theoretical assumption required by the Court's internal consistency test should be extended one step further to permit the use of an entirely theoretical plaintiff.
The State disputes this conclusion, arguing that any internal inconsistency under the AMT cannot be established beyond a reasonable doubt by the use of a hypothetical corporate taxpayer. See In re Haggerty, 448 N.W.2d 363, 364 (Minn.1989) (statutes are presumed constitutional, and constitutional violations must be proven beyond a reasonable doubt). The State maintains that appellants cannot employ an imaginary corporation to prove that the AMT places inconsistent tax burdens upon interstate and intrastate commerce. We agree. Appellants correctly observe that the internal consistency test involves the hypothetical imposition of the same tax by every state. But what is objectionable is appellants' use of a hypothetical plaintiff, X Corporation, to establish a violation of this principle.
The State notes that the Supreme Court has never found a violation of internal consistency by relying upon "the existence of a purely hypothetical taxpayer with a specific structure of factors and taxable income, to justify striking down a tax law which was not facially discriminatory." Despite appellants' insistence that their case is quite similar to several decisions by the Supreme Court, in each of those cases real taxpayers could have suffered discriminatory taxation if the challenged tax scheme was adopted in every state. See, e.g., Armco, Inc. v. Hardesty, 467 U.S. 638, 644, 104 S.Ct. 2620, 2623, 81 L.Ed.2d 540 (1984); Tyler Pipe Indus., Inc. v. Washington Dep't of Revenue, 483 U.S. 232, 107 S.Ct. 2810, 97 L.Ed.2d 199 (1987). Appellants have shown no existing taxpayer with the same financial circumstances as X Corporation, and none of the representative plaintiffs' tax situations reveal a similar constitutional violation.[2] Therefore, we find that *291 the trial court properly rejected the testimony of appellants' mathematical expert and gave his legal conclusions no special weight.

III.
Appellants raise two other arguments on appeal. First, appellants contend that the AMT discriminated against interstate commerce, a violation of the third prong of the Complete Auto test, because it granted a "credit" to those corporations that paid corporate income taxes to Minnesota, but denied this credit to corporations that paid income taxes to other states. See Minn. Stat. § 290.092, subd. 1 (1987) (AMT owed by corporations equals the excess of .001 times the alternative minimum tax base over the regular income-based franchise tax). Therefore, appellants argue, wholly intrastate corporations received preferential treatment under the AMT as compared to interstate corporations. We note, however, that there is no constitutional requirement of a credit for corporate taxes paid to other states.[3] The credit of which appellants complain was simply a mathematical means of ensuring that corporations operating in Minnesota paid either the ordinary income-based tax or the AMT, whichever was greater. Furthermore, all franchise taxes on corporate income, sales, property and payroll were apportioned to the corporation's Minnesota activities without regard to corporate domicile. Thus, appellants have failed to establish that the AMT scheme granted preferential treatment to intrastate businesses at the expense of interstate commerce.
Finally, appellants maintain that the AMT violated the Uniformity Clause of the Minnesota Constitution by creating an unconstitutional classification of corporate taxpayers, and by imposing an additional tax on Minnesota business activities which are already subject to income, real property and unemployment compensation taxes. The Uniformity Clause requires, in pertinent part, that "[t]axes shall be uniform upon the same class of subjects." Minn. Const. art. X, § 1. This provision is no more restrictive upon the legislature's taxing power than the Equal Protection Clause of the Fourteenth Amendment. As this court has stated, "[i]f the statute here involved does not violate one, it does not violate the other." Elwell v. Hennepin County, 301 Minn. 63, 75, 221 N.W.2d 538, 546 (1974).
Minnesota courts apply a three-factor rational basis test to determine the constitutionality of statutory classifications:
(1) The distinctions which separate those included within the classification from those excluded must not be manifestly arbitrary or fanciful but must be genuine and substantial, thereby providing a natural and reasonable basis to justify legislation adapted to peculiar conditions and needs;
(2) the classification must be genuine or relevant to the purpose of the law; that is, there must be an evident connection between the distinctive needs peculiar to the class and the prescribed remedy; (3) the purpose of the statute must be one that the state can legitimately attempt to achieve.
Miller Brewing Co. v. State, 284 N.W.2d 353, 356 (Minn.1979). The district court rejected appellants' argument that the AMT created an unconstitutional classification of corporate taxpayers. The court explained that all corporations are liable for a total franchise tax based on the same Minnesota factors, without regard to a corporation's ability to pay. It further concluded that "any classifications *292 that may exist are genuine and relevant to the purpose of the law and not arbitrary or fanciful."
In their challenge to the district court's conclusion, appellants assert that the AMT is not a uniform tax because it is only imposed upon those corporations with profits insufficient to avoid its application. Nonetheless, we find that the district court's findings were correct: under the rational basis standard set forth in Miller Brewing and the Uniformity Clause, the AMT was not an unconstitutional tax. The State correctly notes that the standard of proof faced by appellants is a considerable barrier to victory in this court. Legislative tax classifications are granted additional deference under the Uniformity Clause, and will be struck down only when absolutely necessary. Guilliams v. Commissioner of Revenue, 299 N.W.2d 138, 142 (Minn.1980); Miller Brewing, supra, at 356. Any classifications created by the AMT must be considered in light of its legislative purpose, which the State defines as "to impose a measure of tax upon corporations which elect to exercise their corporate franchises in Minnesota in a given year."
First, even if the AMT created separate classes of corporate taxpayers, this was a "genuine and substantial" distinction intended to make corporations without significant profits share the burden of supporting public services in Minnesota. Miller Brewing, 284 N.W.2d at 356. Second, the purpose of the AMT was to broaden the corporate franchise tax base. This was reasonably accomplished by the enactment of a new minimum franchise tax applicable to all corporations operating in Minnesota. And third, the purpose of the AMT was legitimately addressed by the legislature. By enacting the new tax scheme, the legislature could require that all corporations, no matter how profitable, contribute to public services and share the corporate tax burden. Furthermore, the AMT was intended to reduce the unpredictability of the solely income-based franchise tax system and increase tax revenues, two indisputably valid legislative goals. In short, the AMT was not an arbitrary or irrational legislative enactment.
Appellants further assert that the AMT constitutes an additional tax on Minnesota factors which are already subject to income, real property and unemployment compensation taxes. Corporations contribute to the public coffers through other types of state taxes, argue appellants, and should not be subjected to an additional franchise tax which most likely exceeds the cost of any public services received. We disagree. The AMT was not an income tax, but a distinctly different tax intended to exact a minimum amount of financial support from corporations that used Minnesota's public services in the course of their business. Therefore, appellants' contention that the AMT imposed an additional tax upon income and corporate sales, payroll and property mischaracterizes the legal basis for the imposition of the AMT. The fact that the AMT considered a corporation's Minnesota sales, property and payroll in calculating the franchise tax owed does not mean that the legislature levied an additional sales, property and income tax on only certain corporations, nor that it has violated the rational basis test established by this court in Miller Brewing. Thus, appellants' final contentions are without merit.
The district court's decision is affirmed.
NOTES
[1]  As noted above, appellants' fair apportionment argument is based upon a hypothetical "X Corporation" with certain income, sales, property and payroll amounts in Minnesota. If X Corporation has a net taxable income of $770,000 in Minnesota in one year, it will have an income-based franchise tax liability (based on a tax rate of 9.5%) of $73,150. This income tax must be compared, however, to X Corporation's alternative minimum tax liability to determine the actual franchise tax owed. Assuming X Corporation operates only within this state and has $11,000,000 in Minnesota sales, $58,200,000 in Minnesota property and $3,700,000 in Minnesota payroll, its AMT liability in Minnesota will be $72,900, or the sum of .001 times each factor. Because its income tax liability exceeds its AMT liability, X Corporation will owe the State the greater amount, or $73,150, in franchise taxes for that year. A different result is reached in certain financial situations, according to appellants, if X Corporation operates in Minnesota and nine other states. Assuming that the AMT statutory scheme is employed by all states, X Corporation could be liable for up to $104,340 in franchise taxes, or 43% more than a wholly intrastate corporation with identical income and factor totals. This is because each individual state will compare X Corporation's income tax liability with its AMT liability and require X Corporation to pay the higher amount, resulting in a different total tax at certain levels of sales, property and payroll than an entirely intrastate corporation.
[2]  In fact, the hypothetical corporation employed by appellants requires a very unusual combination of circumstances to demonstrate any violation at all. The State notes that X Corporation has an unusually low rate of investment return (1.3%) when compared to the average return in even a low profit margin industry, such as wholesale foods (10.7%). Furthermore, if X Corporation's rate of investment return increased to just 3.1%, still a very low rate, no violation of internal consistency would occur.
[3]  Appellants point to Justice Souter's comments in Jefferson Lines in support of their contention that a credit for franchise taxes paid to other states is required under the Commerce Clause. See ___ U.S. at ___ n. 6, 115 S.Ct. at 1342 n. 6. But appellants take Justice Souter's statements out of context. The Supreme Court's decision in Jefferson Lines concerned a sales tax levied on all interstate bus tickets sold in Oklahoma. Id. at ___, 115 S.Ct. at 1335. In upholding Oklahoma's sales tax scheme, Justice Souter, writing for the majority, noted that the Court had never upheld a tax that provided credits for payments of in-state taxes, but denied such credits for payments of equivalent taxes paid to other states. This comment, however, was in reference to sales/use tax schemes which compensate states for sales taxes lost when resident taxpayers purchase goods in foreign states and then transport them into the home state. The AMT is not comparable to the paired or compensating taxation schemes at issue in Jefferson Lines; therefore appellants' reliance on that case is misplaced.
