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Theorem alequcoms 1450
Description: A commutation rule for identical variable specifiers. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
alequcoms.1 (∀𝑥 𝑥 = 𝑦𝜑)
Assertion
Ref Expression
alequcoms (∀𝑦 𝑦 = 𝑥𝜑)

Proof of Theorem alequcoms
StepHypRef Expression
1 alequcom 1449 . 2 (∀𝑦 𝑦 = 𝑥 → ∀𝑥 𝑥 = 𝑦)
2 alequcoms.1 . 2 (∀𝑥 𝑥 = 𝑦𝜑)
31, 2syl 14 1 (∀𝑦 𝑦 = 𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1283
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-10 1437
This theorem is referenced by:  hbae  1647  dral1  1659  drex1  1720  aev  1734  sbequi  1761
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