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Theorem aecoms 2072
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 2071 . 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 1397
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1633  ax-4 1646  ax-5 1719  ax-6 1765  ax-7 1808  ax-10 1855  ax-12 1872  ax-13 2020
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1628  df-nf 1632
This theorem is referenced by:  axc11  2074  nd4  8900  axrepnd  8904  axpownd  8911  axregnd  8914  axregndOLD  8915  axinfnd  8917  axacndlem5  8922  axacnd  8923  wl-ax11-lem1  30230  wl-ax11-lem3  30232  wl-ax11-lem9  30238  wl-ax11-lem10  30239  e2ebind  33715
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