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Theorem alequcom 1680
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.)
Assertion
Ref Expression
alequcom  |-  ( A. x  x  =  y  ->  A. y  y  =  x )

Proof of Theorem alequcom
StepHypRef Expression
1 ax-10 1678 1  |-  ( A. x  x  =  y  ->  A. y  y  =  x )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532
This theorem is referenced by:  alequcoms  1681  nalequcoms  1682  aev  1924  sbcom  1984  alequcomsX  28350  nalequcomsX  28351  a12stdy2  28377
This theorem was proved from axioms:  ax-10 1678
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