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Theorem aecoms 1887
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
aecoms  |-  ( A. y  y  =  x  ->  ph )

Proof of Theorem aecoms
StepHypRef Expression
1 aecom 1886 . 2  |-  ( A. y  y  =  x  ->  A. x  x  =  y )
2 alequcoms.1 . 2  |-  ( A. x  x  =  y  ->  ph )
31, 2syl 15 1  |-  ( A. y  y  =  x  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527
This theorem is referenced by:  hbae  1893  dvelimh  1904  dral1  1905  nd4  8212  axrepnd  8216  axpowndlem3  8221  axpownd  8223  axregnd  8226  axinfnd  8228  axacndlem5  8233  axacnd  8234  e2ebind  28329  a12stdy4  29129
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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