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Theorem aecoms-o 32397
Description: A commutation rule for identical variable specifiers. Version of aecoms 2108 using ax-c11 . (Contributed by NM, 10-May-1993.) (New usage is discouraged.)
Hypothesis
Ref Expression
alequcoms-o.1  |-  ( A. x  x  =  y  ->  ph )
Assertion
Ref Expression
aecoms-o  |-  ( A. y  y  =  x  ->  ph )

Proof of Theorem aecoms-o
StepHypRef Expression
1 aecom-o 32396 . 2  |-  ( A. y  y  =  x  ->  A. x  x  =  y )
2 alequcoms-o.1 . 2  |-  ( A. x  x  =  y  ->  ph )
31, 2syl 17 1  |-  ( A. y  y  =  x  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1436
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-c11 32384
This theorem depends on definitions:  df-bi 189  df-ex 1661
This theorem is referenced by:  hbae-o  32398  dral1-o  32399  dvelimf-o  32425  aev-o  32427  ax12indalem  32441  ax12inda2ALT  32442
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