
814 P.2d 863 (1991)
ALLSTATE INSURANCE COMPANY, Plaintiff-Appellee,
v.
Emile FEGHALI and Sirvart Feghali, Defendants-Appellants.
No. 90SA87.
Supreme Court of Colorado, En Banc.
July 9, 1991.
*864 Robert A. Zupkus, Stefan Kazmierski, Zupkus & Ayd, P.C., Denver, for plaintiff-appellee.
Arnold D. Barrish, Wheat Ridge, for defendant-appellant Emile Feghali.
Sirvart Feghali, Aurora, pro se.
*865 Mark T. Hamby, Ozer, Trueax & Kullmann, P.C., Denver, for amicus curiae Colorado Trial Lawyers Ass'n.
Thomas J. Seaman, David P. Reiter, Creamer and Seaman, P.C., Denver, for amicus curiae Colorado Defense Lawyers Ass'n.
Justice MULLARKEY delivered the Opinion of the Court.
In January, 1987, appellants Emile Feghali and Sirvart Feghali, husband and wife, were driving separate vehicles and were involved in an accident between the two vehicles. The Feghalis resided in the same household and the automobiles were insured by appellee Allstate Insurance Company ("Allstate") under the same policy. Mr. Feghali filed suit against Ms. Feghali, alleging injuries and seeking damages resulting from the accident. Allstate filed a complaint for declaratory judgment, seeking a determination that it had no duty to defend or indemnify Ms. Feghali because of a "household exclusion" in the insurance policy.[1] By counterclaim, Mr. Feghali argued that if his wife was not entitled to liability coverage due to the household exclusion, Mr. Feghali should be entitled to uninsured motorist benefits under the policy. The trial court ruled in favor of Allstate on all claims and issues.
The Feghalis appealed directly to this court[2] and contend here that the household exclusion violates the purpose and policy of the Colorado Auto Accident Reparations Act, section 10-4-701, et seq., 4A C.R.S. (1987 & 1990 Supp.) (the "Act"). The Feghalis also argue that if we find that the household exclusion is consistent with the Act based on section 10-4-418(2)(b), 4A C.R.S. (1987), section 10-4-418(2)(b) is unconstitutional because it violates the Feghalis' rights to equal protection under both the Colorado Constitution and the United States Constitution. Finally, Mr. Feghali argues that, if the household exclusion is valid, Mr. Feghali is entitled to coverage under the uninsured motorist protection of the policy.[3] We resolve all issues in favor of Allstate.

I.
We held in Meyer v. State Farm Mut. Auto. Ins. Co., 689 P.2d 585 (Colo.1984), that the household exclusion clauses in that case were invalid because they violated the public policy of compulsory liability insurance required by the Act. Meyer, 689 P.2d at 589. After we decided Meyer, the General Assembly enacted section 10-4-418(2)(b), 4A C.R.S. (1987), which states as follows:
The commissioner [of insurance] shall not find that a policy form, certificate, or contract of insurance or rider does not comply with the applicable requirements and standards of this title [10, Insurance,] on the ground that it excludes coverage of claims made by a member of a household against another member of the same household. Such exclusions are in conformity with the public policy of this state.
We then held in Schlessinger v. Schlessinger, 796 P.2d 1385 (Colo.1990), that the General Assembly legislatively repealed the Meyer decision by enacting section 10-4-418(2)(b). We stated:
In our view, the General Assembly's enactment of section 10-4-418(2)(b) is a clear signal that this court's interpretation of the legislative declaration of purpose in the Auto Accident Reparations Act [in Meyer ] did not correspond to the purpose actually intended by the General Assembly. [T]he General Assembly[] determin[ed] that the public policy underlying the Auto Accident Reparations Act was not intended to abrogate the household *866 exclusion clause in automobile liability policies....
Schlessinger, 796 P.2d at 1389.

A.
Schlessinger is dispositive of the Feghalis' claim that the household exclusion in their policy violates the purpose and policy of the Act. We decided in Schlessinger that the holding in Meyer that household exclusions violated the policy and purpose of the Act was repealed by the adoption of section 10-4-418(2)(b). We see no reason to reconsider that decision. Section 10-4-418(2)(b) legislatively authorized the use of household exclusions in automobile liability policies and household exclusions therefore are consistent with the public policy of the Act.

B.
The parties agree that, because there is no fundamental right or suspect class at issue, the rational basis test applies to the Feghalis' equal protection challenge to section 10-4-418(2)(b). See, e.g., Austin v. Litvak, 682 P.2d 41, 49 (Colo.1984). To satisfy the rational basis test, the statutory classification must have some rational basis in fact and be reasonably related to a legitimate government interest. Id. at 50. The burden of proof is on the party challenging the statute to show beyond a reasonable doubt that the statute is unconstitutional. See, e.g., City of Montrose v. Public Utilities Comm'n, 732 P.2d 1181, 1189 (Colo.1987).
There are a number of justifications offered for the use of household exclusions. The primary justification offered "is to prevent suspect inter-family legal actions which may not be truly adversary and over which the insurer has little or no control. [Thus,] [s]uch ... exclusion[s] [are] a natural target for the insurer's protection from collusive assertions of liability." Farmers Ins. Exch. v. Cocking, 29 Cal.3d 383, 389, 173 Cal.Rptr. 846, 849, 628 P.2d 1, 4 (1981) (quoting United Farm Bureau Mut. Ins. Co. v. Hanley, 172 Ind.App. 329, 360 N.E.2d 247, 252 (1977)).[4]
Given the possibility of collusion, the California Supreme Court has pointed out that the permission of household exclusion clauses also may serve to benefit the public. In Farmers Ins. Exch., that court stated:
The Legislature reasonably may have concluded that the benefits to the public from automatically including "family member" coverage in all automobile liability policies were outweighed by the probable adverse consequences of such a rule. It is not unreasonable to suppose that substantial increases in premiums would be forthcoming if such coverage were declared mandatory. It may well have been a legislative concern that an increase in the costs of liability insurance might result in an appreciable increase in the number of uninsured drivers to the ultimate detriment of the general public.
Farmers Ins. Exch., 29 Cal.3d at 390, 173 Cal.Rptr. at 849, 628 P.2d at 4 (emphasis in original). Finally, Professor Widiss has argued that the possibility of disrupting the family by litigation among family members probably is the most important justification for intra-family tort immunity in automobile insurance policies. A. Widiss, Uninsured and Underinsured Motorist Insurance § 4:19 (2d ed. 1990).
These justifications for permitting household exclusions are legitimate government *867 objectives which the legislature reasonably may have pursued in enacting section 10-4-418(2)(b). Given these justifications, it is reasonable to distinguish between plaintiffs "related by blood, marriage, or adoption to an insured against whom claim is made if such person resides in the same household as such insured" and plaintiffs who are unrelated or who do not reside in the same household.[5] Thus, section 10-4-418(2)(b) does not violate the Feghalis' right to equal protection under either the Colorado or the United States Constitutions.

II.
Mr. Feghali also contends that, given a holding that Ms. Feghali is not entitled to liability coverage because of the household exclusion, she was an uninsured motorist and Mr. Feghali is entitled to uninsured motorist benefits under the policy. Mr. Feghali makes two arguments in support of this contention. Mr. Feghali initially contends that denying uninsured motorist benefits to him would contravene the legislative intent and policy of section 10-4-609, 4A C.R.S. (1987) (insurance protection against uninsured motorists). Mr. Feghali also argues that the terms of the Feghalis' policy do not exclude him from uninsured motorist protection. We address each argument in turn.

A.
In Terranova v. State Farm Mut. Auto. Ins. Co., 800 P.2d 58 (Colo.1990), we held that "the exclusion of a vehicle insured under the liability terms of a policy from uninsured motor vehicle coverage does not violate the legislative purposes and the public policy underlying section 10-4-609." Terranova, 800 P.2d at 62. Although Terranova did not involve the denial of liability coverage under a household exclusion, we stated as follows:
A claim for uninsured motorist benefits is often predicated on a denial of liability coverage pursuant to a household exclusion. Such a household exclusion would be ineffectual in an automobile liability policy if the insured vehicle exclusion is found to be void as against public policy. Such a finding would be in direct contravention of the explicit statement of legislative policy contained in section 10-4-418(2)(b). See Schlessinger v. Schlessinger, 796 P.2d 1385 (Colo.1990) (abolition of Colorado's doctrine of limited parental immunity in the context of a negligence-based claim for uninsured motorist benefits would contradict the public policy embodied in section 10-4-418(2)(b)).
Id. at 62 n. 4 (citation omitted). As this language from Terranova makes clear, it would contravene the express legislative intent of permitting household exclusions if we were to hold that uninsured motorist protection is available when (a) a policy excludes from uninsured motorist protection an automobile insured under the policy's liability coverage and (b) the policy denies liability coverage under a household exclusion. Such a holding would nullify the legislatively-sanctioned household exclusion. We therefore reject Mr. Feghali's argument that legislative intent requires us to permit recovery of uninsured motorist benefits if liability coverage is denied under a valid household exclusion.

B.
The parties agree that the policy limits uninsured motorist coverage to bodily *868 injury resulting from accidents involving an "uninsured automobile" and that the policy specifically excludes an "insured automobile" from the definition of an "uninsured automobile." The question is whether Ms. Feghali's automobile was an "insured automobile" at the time of the accident. The relevant section of the policy includes in its definition of an "insured automobile" an automobile "described in the declarations as an insured automobile to which the bodily injury coverage of the policy applies." The automobile Ms. Feghali was driving at the time of the accident was included in the declarations as an "insured automobile." Mr. Feghali nonetheless argues that the denial of liability coverage to Ms. Feghali prevents her automobile from being considered an "insured automobile" at the time of the accident.
We reject Mr. Feghali's construction of the policy. The listing of the automobile in the declarations as an insured automobile means that Ms. Feghali's automobile was within the policy's liability coverage. The fact that Ms. Feghali is denied liability coverage because of the household exclusion does not transform her insured automobile into an uninsured automobile. See, e.g., Phyall v. Allstate Ins. Co., 551 So.2d 303, 304 (Ala.1989) (an automobile insured under the liability coverage of the policy does not become uninsured because liability coverage is not available to a particular individual due to a household exclusion); Reid v. Allstate Ins. Co., 352 So.2d 1172, 1173 (Fla.1978) (vehicle insured under the liability coverage of the policy "does not become uninsured because liability coverage may not be available to a particular individual" due to a household exclusion); Frye v. Frye, 305 Md. 542, 505 A.2d 826, 839 (1986) (a vehicle covered under the liability portion of the policy "was not transformed into an uninsured vehicle because the father was immune to an action in negligence by the son").[6]
Although Terranova is not dispositive of Mr. Feghali's claim that he is entitled to uninsured motorist protection in this case,[7]Terranova provides additional support for our holding that Mr. Feghali is not entitled to uninsured motorist protection. As discussed above, we held in Terranova that the denial of uninsured motorist protection to a vehicle insured under an insurance policy's liability coverage did not violate public policy. Terranova, 800 P.2d at 62. In support of this holding, we pointed out that to hold that exclusions of insured vehicles from uninsured motorist coverage were void, thus permitting recovery under uninsured motorist coverage where a household exclusion had precluded liability coverage, would contravene the legislative policy of section 10-4-418(2)(b). Id. at 62 n. 4. Construing the policy's definition of an "insured automobile" as not including an automobile for which liability coverage was denied under the household exclusion would yield the same result. The insured would be permitted to recover uninsured motorist benefits despite the household exclusion, thus contravening the policy of section 10-4-418(2)(b). We refuse to permit this contravention of legislative policy.

III.
In summary, we hold that the use of household exclusions in automobile liability policies was legislatively authorized by section *869 10-4-418(2)(b), and household exclusions therefore do not violate public policy. Section 10-4-418(2)(b) does not violate the Feghalis' right to equal protection under either the Colorado or United States Constitutions. We also hold that Mr. Feghali is not entitled to uninsured motorist benefits. Public policy does not require that Mr. Feghali receive uninsured motorist benefits and the Feghalis' insurance policy specifically excluded him from uninsured motorist protection.
Judgment affirmed.
ERICKSON, J., does not participate.
NOTES
[1]  The household exclusion stated that the liability insurance coverage did not apply to "bodily injury to any person who is related by blood, marriage, or adoption to an insured against whom claim is made if such person resides in the same household as such insured."
[2]  We have jurisdiction of this appeal under C.A.R. 1 and § 13-4-102(1)(b), 6A C.R.S. (1987), because of the constitutional issues raised by the Feghalis.
[3]  The parties agree that Mr. Feghali is entitled to personal injury protection benefits under the policy.
[4]  The Feghalis argue that the prevention of collusion is an insufficient justification because we discounted the collusion argument in Meyer. See Meyer, 689 P.2d at 591. This argument is misplaced, however, because our task in Meyer was to discern whether the public policy of the Act permitted household exclusions. Here, the legislature has rejected our interpretation in Meyer and our task is limited to deciding whether the legislature's decision to permit household exclusions was rational. Thus, while we discounted the validity of the collusion argument in assessing the policy of the Act in Meyer, the legislature was free to accept this rationale in passing section 10-4-418(2)(b). Indeed, we acknowledged in Meyer that a legislature might accept the collusion argument. We distinguished Farmers Ins. Exch. on the grounds that "the California Supreme Court [there] held that a statute which permit[ted] an automobile liability insurer to exclude coverage for bodily injuries to an insured [was] neither contrary to public policy nor [did] it deny equal protection." Meyer, 689 P.2d at 590 (emphasis in original).
[5]  The Feghalis argued at oral argument that section 10-4-418(2)(b) is overinclusive because it creates an "irrebuttable presumption of collusion" as to parties subject to the household exclusion, thus precluding recovery by people who would not collude. The Feghalis misinterpret the section. Section 10-4-418(2)(b) does not create any such presumption because the section does not require household exclusions. See § 10-4-418(2)(b). Section 10-4-418(2)(b) merely permits an insurer and an insured to agree to household exclusions in the insurance policy. Id. In addition, "in almost all cases, the classification will not be perfectly efficient, but will be either `overinclusive' or `underinclusive' or both." G. Stone, L. Seidman, C. Sunstein, M. Tushnet, Constitutional Law 502 (1986). Mathematical precision is not required. It is well recognized that "[legislative] reform may take one step at a time, addressing itself to the phase of the problem which seems most acute to the legislative mind. The legislature may select one phase of one field and apply a remedy there, neglecting the others." Williamson v. Lee Optical, 348 U.S. 483, 489, 75 S.Ct. 461, 465, 99 L.Ed. 563 (1955) (citation omitted).
[6]  Mr. Feghali cites several cases where an insured was permitted to recover uninsured motorist benefits where liability coverage was denied under a household exclusion. See, e.g., State Farm Mut. Auto. Ins. Co. v. Herron, 123 Ariz. 315, 599 P.2d 768 (1979); Barnes v. Powell, 49 Ill.2d 449, 275 N.E.2d 377 (Ill.1971); Rodman v. State Farm Mut. Auto. Ins. Co., 208 N.W.2d 903 (Iowa 1973); Bowsher v. State Farm Fire and Casualty Co., 244 Or. 549, 419 P.2d 606 (1966). Most of these decisions, however, are based on policies underlying the uninsured motorist statutes of the states in which the cases were decided. Because we hold that it would contravene the policy underlying section 10-4-418(2)(b) to permit an insured to recover uninsured motorist benefits where liability coverage is denied under a household exclusion, these cases are inapposite here. But cf. Faraj v. Allstate Ins. Co., 486 A.2d 582 (R.I.1984) (child permitted to recover under the uninsured motor vehicle coverage of father's policy because child was not entitled to liability coverage under the policy due to a household exclusion).
[7]  As mentioned above, Terranova did not involve the denial of liability coverage under a household exclusion.
