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Theorem alequcom 1408
Description: Commutation law for identical variable specifiers. The antecedent and consequent are true when 𝑥 and 𝑦 are substituted with the same variable. Lemma L12 in [Megill] p. 445 (p. 12 of the preprint). (Contributed by NM, 5-Aug-1993.)
Ref Expression
alequcom (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)

Proof of Theorem alequcom
StepHypRef Expression
1 ax-10 1396 1 (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1241
This theorem was proved from axioms:  ax-10 1396
This theorem is referenced by:  alequcoms  1409  nalequcoms  1410  aev  1693
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