
530 So.2d 475 (1988)
KIDDER ELECTRIC OF FLORIDA, INC., Appellant,
v.
UNITED STATES FIDELITY & GUARANTY CO., Appellee.
No. 88-528.
District Court of Appeal of Florida, Fifth District.
September 1, 1988.
Joseph A. Lane of Lowndes, Drosdick, Doster, Kantor & Reed, Professional Ass'n, Orlando, for appellant.
Jon M. Wilson and Andrew V. Showen of Foley & Lardner, Van Den Berg, Gay, *476 Burke, Wilson & Arkin, Orlando, for appellee.
COWART, Judge.
A general contractor (Jendoco) provided an owner (Healthnet) with a payment bond (with the contractor as principal) and USF & G as surety, for the use and benefit of persons supplying labor and material in performance of a construction contract to improve the owner's real property. (See § 713.23(1)(a), Fla. Stat.). An electrical subcontract between the general contractor and a subcontractor (appellant Kidder Electric of Florida, Inc.) contained a provision for arbitration of controversies arising between the parties thereto.
When a controversy arose between the subcontractor and the general contractor, the subcontractor instituted an arbitration proceeding by filing an appropriate demand for arbitration with a designated arbitration association to which the general contractor responded. Apparently because the general contractor did not neglect to or refuse to comply with the provision for arbitration, the subcontractor did not need to, and therefore did not, "make application to the court for an order directing the parties to proceed with arbitration" as permitted under section 682.03(1), Florida Statutes. Thereafter, to toll the statute of limitations (§ 713.23(1)(f), Fla. Stat.) the subcontractor filed its action against the surety on the payment bond. In its complaint the subcontractor moved to stay the bond action against the surety until the conclusion of the pending arbitration proceeding.
The general contractor, as intervenor in the bond action, and the surety company jointly moved to stay the arbitration proceeding until the conclusion of the bond litigation. In this joint motion to stay, it was alleged that because the general contractor, as principal on the bond, was liable to the surety in the event the subcontractor recovered on the surety bond, the general contractor was a real party in interest in the bond litigation and had agreed to defend the bond action on behalf of the surety. The trial court granted the motion of the general contractor and surety and ordered a stay of the arbitration proceeding. The subcontractor appeals. We reverse.
The ultimate issue in the arbitration proceeding is whether the subcontractor is entitled to payment from the contractor for labor and materials furnished by the subcontractor to improve the owner's real property under the construction contract between the contractor and the owner. Because, in this case, the surety has actual notice of the arbitration proceeding whether or not the surety chooses to participate in the arbitration proceeding  the surety will be bound by an arbitration determination that its principal (the contractor) is liable to the subcontractor and the subcontractor will be entitled to an order confirming any arbitration award in its favor, not only as against the contractor but also against the surety (see Von Engineering Co. v. R.W. Roberts Construction Co., Inc., 457 So.2d 1080 (Fla. 5th DCA 1984)) and the need for litigation on the bond will be obviated. See also Graham Contracting, Inc. v. Flagler County, 458 So.2d 418 (Fla. 5th DCA 1984). On the other hand, because the surety is responsible on the payment bond only if the subcontractor is entitled to payment from the contractor for labor and material improving the owner's real property, a determination in the arbitration proceeding that the contractor is not liable to the subcontractor will necessarily be a determination that the subcontractor is not entitled to recover on the payment bond under the doctrine of collateral estoppel, and that determination will bind the subcontractor in the bond action and the need for litigation on the bond will be obviated.[1] Thus, in this case, in either turn of events, the arbitration determination will eliminate the issue in the bond litigation. Therefore, in order to effectuate the arbitration provision in the contract between the contractor and the subcontractor *477 and to permit the subcontractor to toll the statute of limitations on its cause of action on the bond and to avoid unnecessary litigation, the arbitration proceeding should be permitted to proceed and the bond litigation should be stayed. While the surety has never agreed to arbitrate any claim against it on its bond, nevertheless, the surety's principal (the contractor) has agreed with the subcontractor to arbitrate what is essentially the same claim.
By filing action on the bond, the subcontractor neither waived its contractual right to arbitrate its controversy with the contractor, nor did it make any election of remedies.[2]
Section 682.03(3), Florida Statutes, is inapplicable to this litigation for several reasons, including the fact that no order for arbitration or application for such order was made in this case, which is a clear condition precedent to the application of that statute.
The order staying the arbitration proceeding is reversed with directions to enter an order staying the litigation on the bond until the conclusion of the arbitration proceeding.
REVERSED and REMANDED.
SHARP, C.J., and COBB, J., concur.
NOTES
[1]  In Post Tensioned Engineering Corp. v. Fairways Plaza Associates, 429 So.2d 1212 (Fla. 3d DCA 1983), the contract between the owner and the general contractor contained an arbitration provision. A contract between the general contractor and certain subcontractors did not contain an arbitration provision. The owner sued the general contractor and the subcontractors alleging negligently performed, defective work. The contractor invoked the arbitration provision. The trial judge denied a stay of the owner's arbitration against the subcontractors because there was no arbitration provision applicable to those parties. The appellate court reversed, directing a stay of the owner's litigation against the subcontractors pending the outcome of the arbitration proceeding between the owner and general contractor because a determination in arbitration that the contractor, as respondeat superior, was not negligent would necessarily be a determination that the subcontractors were not negligent and, therefore, the litigation between the owner and subcontractors "would be obviated." The opinion in Fairways does not consider the other turn of events, i.e., that a determination in arbitration that the contractor was negligent would not determine the owner's litigation against the subcontractors. Even if the contractor prevailed in arbitration, the litigation between the owner and subcontractors would not be "obviated" unless the subcontractors could, under the doctrine of collateral estoppel, defensively assert the arbitration finding against the owner in the litigation. As the subcontractors were not parties to the arbitration proceeding, and therefore not bound by its result, they would not be entitled to assert the arbitration result against the owner if the mutuality rule is applied. The mutuality rule appears to be an outmoded minority view but one that prevails in Florida. See Hill v. Colonial Enterprises, Inc., 219 So.2d 51 (Fla. 4th DCA 1969), cert. discharged, 227 So.2d 481 (Fla. 1969), cited in Annotation, Mutuality of Estoppel as Prerequisite of Availability of Doctrine of Collateral Estoppel to a Stranger to the Judgment, 31 A.L.R.3d at 1062. See also Husky Industries, Inc. v. Griffith, 422 So.2d 996 (Fla. 5th DCA 1982); Newport Div., Tenneco Chemicals, Inc. v. Thompson, 330 So.2d 826 (Fla. 1st DCA 1976). In Fairways, the relationship between the parties is not such as to constitute exception to the mutuality rule. However, in this case, the relationship between the contractor, as principal on the payment bond, and the surety is such that the surety will be bound by the arbitration determination although not a party to the arbitration proceeding. See Von Engineering, supra. Therefore, the mutuality rule is met and both the surety and the subcontractors (who are parties to the arbitration proceeding) will, by the doctrine of collateral estoppel, be bound in the bond action by the determination in the arbitration proceeding.
[2]  In an analogous case, U.S. v. Weiss Pollution Control Corp., 532 F.2d 1009 (5th Cir.1976), the U.S. 5th Circuit Court of Appeals reversed a dismissal of a Miller Act suit (Miller Act, 40 U.S.C. § 270a, et seq., controls payment bonds relating to construction contracts with the United States government). A subcontractor issued a demand for arbitration against the contractor for a dispute on a subcontract which provided for arbitration. The subcontractor also instituted a suit on the Miller Act bond against the surety. The contractor and surety both filed motions to dismiss the bond suit, or in the alternative, stay the proceedings. The subcontractor consented to an order staying the suit on the bond. The trial court, in dismissing the bond suit, treated the subcontractor's demand for arbitration as a waiver of its Miller Act remedy. In reversing, the Fifth Circuit Court of Appeals held that (1) the subcontractor's demand for arbitration did not waive its right to pursue its Miller Act remedy; and (2) the subcontractor's Miller Act suit was not barred by an election of remedies because the arbitration and the suit on the Miller bond were not inconsistent. The court determined that a stay of the bond suit, which was agreed to by the subcontractor, was more appropriate than a dismissal of the bond suit.
