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Theorem alequcoms 1481
Description: A commutation rule for identical variable specifiers. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
alequcoms.1  |-  ( A. x  x  =  y  ->  ph )
Assertion
Ref Expression
alequcoms  |-  ( A. y  y  =  x  ->  ph )

Proof of Theorem alequcoms
StepHypRef Expression
1 alequcom 1480 . 2  |-  ( A. y  y  =  x  ->  A. x  x  =  y )
2 alequcoms.1 . 2  |-  ( A. x  x  =  y  ->  ph )
31, 2syl 14 1  |-  ( A. y  y  =  x  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1314
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-10 1468
This theorem is referenced by:  hbae  1681  dral1  1693  drex1  1754  aev  1768  sbequi  1795
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