Suppose Brian does not send the revocation to Brianna. Even so, he buys the other condo. Brianna, who happens to know the seller of that condo, learns from him that Brian has purchased his condo. Briana is well aware that Brian only wants to purchase one condo. Brianna's learning of Brian's purchase terminates Brian's offer.
The rule is that an offeree can no longer accept an offer if (1) the offeror acts in a way inconsistent with the intention to enter the bargain proposed in that offer, and (2) the offeree learns of the offeror's action from a reliable source. See Restatement (Second) Contracts ยง 43.