The proof Russel gives is better though, because it captures something essential in why "0=1" and "1=2" are wrong via a natural example in sets. Meanwhile you're effectively invoking in Axiom 1 the principle of explosion, which has some intuition to it—being that since there can be no valid proofs of falsehood, we can derive anything on the basis of case analysis on the possible ways (of which there are zero) we could have derived a falsehood—but not quite as nice as what Russel shows.