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Theorem aecoms 2157
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 2156 . 2  |-  ( A. y  y  =  x  <->  A. x  x  =  y )
2 aecoms.1 . 2  |-  ( A. x  x  =  y  ->  ph )
31, 2sylbi 200 1  |-  ( A. y  y  =  x  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-10 1926  ax-12 1944  ax-13 2102
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1675  df-nf 1679
This theorem is referenced by:  axc11  2159  nd4  9046  axrepnd  9050  axpownd  9057  axregnd  9060  axinfnd  9062  axacndlem5  9067  axacnd  9068  wl-ax11-lem1  31961  wl-ax11-lem3  31963  wl-ax11-lem9  31969  wl-ax11-lem10  31970  e2ebind  36975
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