
203 Cal.App.2d 579 (1962)
MITCHELL DAVIES, Plaintiff and Respondent,
v.
PATRICK J. LANGIN, Defendant and Appellant.
Civ. No. 19517. 
California Court of Appeals. First Dist., Div. Two.  
May 16, 1962.
 William Berger and George Olshausen for Defendant and Appellant.
 Young, Rabinowitz & Chouteau and Walter C. Chouteau for Plaintiff and Respondent.
 SHOEMAKER, J.
 This is an appeal by defendant Patrick J. Langin from a judgment awarding plaintiff Mitchell Davies specific performance of a contract to convey real property.
 The facts are as follows: Defendant was the owner of certain real property. Plaintiff became interested in the purchase of the property and asked Lane, a real estate agent, to see the defendant about a possible sale. After Lane saw defendant and ascertained that he was willing to sell, plaintiff executed a uniform deposit receipt in the form of an offer to purchase the property for $21,000. Lane took the offer to the defendant, who stated that the price was not high enough. After discussion between defendant and Lane, the defendant agreed that $21,375 would be an acceptable price if he could remove certain personal property from the premises. On November 5, 1958, the following language was inscribed on the back of the deposit receipt and signed by the defendant:
 "Nov. 5, 1958."
 "I will accept the offer on the reverse with the exception of the price which is to be $21,375. I reserve the right to remove the wall heater in Apt. #1. ..."
 "I agree to leave this offer open for 2 days."
 "Patrick J. Langin."
 The defendant then gave the document to Lane, who took it to the plaintiff on the following day. Plaintiff signed the document below the date, "Nov. 6, 1958" and the words *582 "Above conditions accepted," and gave Lane a check for $1,000 made out to his real estate firm, Trevor and Company.
 Lane, after several unsuccessful attempts, finally reached the defendant by telephone on November 10 or 11, at which time the defendant indicated that he was pleased that the deal had been closed. Lane informed the defendant that he could have until December 15, 1958, to remove his personal property from the premises and also asked him to bring any papers pertaining to the property to the Trevor and Company offices.
 The defendant thereafter brought a tax bill and an insurance policy into the real estate office, left the papers with Mr. Gibson, a partner in Trevor and Company, and stated that he had brought them in for use in closing the transaction.
 Defendant's sole defense to this action is that the plaintiff did not accept the offer within the two days provided in the offer.
 After a trial without jury, the court found that the plaintiff had signed a written acceptance of defendant's offer on November 6, 1958, but had failed to communicate this acceptance to the defendant until several days later. The court further found that after the offer had been communicated to defendant, he waived the delay. The court thereupon awarded specific performance in favor of plaintiff.
 [1] Appellant's first contention is that the trial judge was guilty of prejudicial error in making certain comments during the course of the trial. In support of his position, appellant cites three jury cases setting forth the general rule that a judge should conduct a trial in a fair and impartial manner (Etzel v. Rosenbloom (1948) 83 Cal.App.2d 758, 762 [189 P.2d 848]); that he should not be discourteous toward witnesses (People v. Williams (1942) 55 Cal.App.2d 696, 703 [131 P.2d 851]); and that he should not indicate to the jury that his sympathies lie with one side rather than another (Davis v. Pezel (1933) 131 Cal.App. 46, 54 [20 P.2d 982]). Appellant also relies on the nonjury case of McVey v. McVey (1955) 132 Cal.App.2d 120, 123 [281 P.2d 898], where the court stated that a trial judge should not prejudge the issues but should keep an open mind until all of the evidence is presented to him.
 Our examination of the record convinces us that none of the authorities cited by appellant have any bearing on the instant appeal. It must first be noted that the trial below was not had before a jury. Furthermore, neither of the remarks of which appellant complains indicates that the trial *583 judge had closed his mind or prejudged the case in favor of respondent.
 [2] Appellant next contends that the trial court erred in admitting into evidence that portion of the purchase and sale agreement consisting of respondent's signature and the date, November 6, 1958. It is appellant's position that respondent, by writing this date upon the document, executed a self-serving declaration that he had in fact accepted appellant's offer within the specified two days. Appellant maintains that such a declaration is inadmissible hearsay and that the trial court committed prejudicial error when it overruled his objection and admitted this portion of the document into evidence. This argument has no merit. Under appellant's interpretation of the hearsay rule, virtually any contract or other written instrument would be subject to exclusion as hearsay. Such is clearly not the law. Under the California rule, as set forth by Code of Civil Procedure, section 1963, subdivision 23, a date inscribed upon a writing is not only admissible as evidence but creates a disputable presumption that the instrument was in fact executed upon the date appearing on its face. There can be no doubt that the trial court properly overruled appellant's objection and admitted the entire document into evidence.
 [3] Appellant next asserts that the trial court erred when it sustained respondent's objection to a question directed by appellant's counsel to Lane, as to whether he knew "that the offer as contained in the back of this must be within two days of November the 5th."
 The record reveals that appellant's counsel managed through subsequent questioning to elicit the information sought, but that he himself chose to strike that portion of the witness' testimony covering the matter. There was no prejudicial error in the ruling.
 [4a] Appellant next contends that the trial court was not entitled to base its judgment on the finding that appellant waived the two-day requirement, since respondent failed to plead this theory in his complaint.
 [5] Although it is true that a special defense such as estoppel or waiver generally cannot be proved unless pleaded, this rule does not apply where evidence of such a defense is made relevant by a contention raised in the answer. (See 2 Witkin, California Procedure,  548- 549, pp. 1546-1548; Llewellyn Iron Works v. Abbott Kinney Co. (1916) 172 Cal. 210, 213 [155 P. 986]; Fanning v. Yoland Productions, Inc. *584 (1957) 150 Cal.App.2d 444, 452 [310 P.2d 85]; Clevenger v. Clevenger (1961) 189 Cal.App.2d 658, 673-674 [11 Cal.Rptr. 707].) [4b] In the case at bar, respondent alleged in his complaint that he had accepted appellant's offer on November 6, 1958. Appellant denied this allegation in his answer, asserting there had been no acceptance within the two-day period set forth in the offer. By so doing, appellant raised the issue which invited the application of the doctrine of waiver. Furthermore, appellant, in his pretrial statement, expressly denied that he had ever heard from respondent or anyone on his behalf until 12 to 15 days after the offer had been made, and that he then advised respondent's broker that "the offer had expired and that the issue was closed." In view of this assertion, appellant certainly cannot contend that he was taken by surprise or otherwise prejudiced when respondent offered evidence tending to prove that appellant had been informed of the acceptance at an earlier date and that he had at that time indicated that the contract was agreeable to him.
 [6] The sole remaining question to be resolved is whether the evidence was sufficient to support the trial court's finding that appellant did in fact waive the two-day requirement.
 The facts which we have recited at the outset of this opinion clearly show that appellant made no attempt to rely upon the two-day requirement provided in his offer, but, on the contrary, indicated that an acceptance made at a later date was entirely agreeable to him. Under these circumstances, it cannot be said that the trial court erred in finding that appellant waived compliance with the two-day acceptance requirement of the offer.
 Appellant seriously urges, however, that an option which is not accepted within the time limit set comes to an end, and that no waiver on the part of the optionor can revive a right which is already lost. Such an argument is of little relevance in view of the fact that appellant's offer was clearly not an option. [7] The rule is well established that an offer which states that it will remain open for a given length of time may nevertheless be withdrawn at any time prior to acceptance unless based upon a valuable consideration. (Christy v. Drapeau (1937) 22 Cal.App.2d 582, 587 [71 P.2d 940].) In our case, there was no evidence whatever that any consideration passed from respondent to appellant in return for appellant's promise to hold his offer open for two days. [8] In accordance with the general rules governing contracts, an offer which contains no specified time limit is *585 revoked by operation of law by the lapse of an unreasonable period of time. (Westwood v. Franklin (1946) 77 Cal.App.2d 189 [175 P.2d 58].) [9] Where the offer does contain such a time limitation, revocation occurs upon the expiration of the period specified. (Gibbs v. Peters (1927) 82 Cal.App. 407, 410 [255 P. 521].) In either case, the end result is the expiration or revocation of the offer and the creation of a right on the part of the offeror to refuse to recognize a belated acceptance. In Forbes v. Board of Missions (1941) 17 Cal.2d 332 [110 P.2d 3], the court held that this right was waived by an offeror who chose to ignore the delay and treat the acceptance as timely. The same reasoning would appear equally applicable to the case at bar.
 [10] While there is thus ample evidentiary support for the trial court's finding that appellant waived the two-day acceptance requirement set forth in his offer, in our view there was no necessity for the court to base its judgment for specific performance upon this ground. The trial court's finding that respondent's acceptance was not communicated to appellant within the required two days is not supported by the evidence, for it is undisputed that appellant gave the written offer to Lane for transmittal to respondent and that he was successful in obtaining respondent's written acceptance within the prescribed two days. Under such circumstances, the law is clear that Lane was appellant's agent to consummate the sale and a valid contract was formed when respondent tendered his signed acceptance to him. (Ussery v. Jackson (1947) 78 Cal.App.2d 355 [177 P.2d 970]; Bellasi v. Shackelford (1962) 201 Cal.App.2d 265 [19 Cal.Rptr. 925].)
 Respondent's right to specific performance being clearly established, the judgment is affirmed.
 Kaufman, P. J., and Agee, J., concurred.
