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Theorem aecoms 2012
Description: A commutation rule for identical variable specifiers. (Contributed by NM, 10-May-1993.)
Hypothesis
Ref Expression
aecoms.1  |-  ( A. x  x  =  y  ->  ph )
Assertion
Ref Expression
aecoms  |-  ( A. y  y  =  x  ->  ph )

Proof of Theorem aecoms
StepHypRef Expression
1 aecom 2011 . 2  |-  ( A. y  y  =  x  <->  A. x  x  =  y )
2 aecoms.1 . 2  |-  ( A. x  x  =  y  ->  ph )
31, 2sylbi 195 1  |-  ( A. y  y  =  x  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1368
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-12 1794  ax-13 1955
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591
This theorem is referenced by:  axc11  2014  nd4  8866  axrepnd  8870  axpowndlem3OLD  8877  axpownd  8879  axregnd  8882  axregndOLD  8883  axinfnd  8885  axacndlem5  8890  axacnd  8891  wl-ax11-lem1  28550  wl-ax11-lem3  28552  wl-ax11-lem9  28558  wl-ax11-lem10  28559  e2ebind  31605
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