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Theorem aecoms 2111
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 2110 . 2  |-  ( A. y  y  =  x  <->  A. x  x  =  y )
2 aecoms.1 . 2  |-  ( A. x  x  =  y  ->  ph )
31, 2sylbi 198 1  |-  ( A. y  y  =  x  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909  ax-13 2057
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662
This theorem is referenced by:  axc11  2113  nd4  9022  axrepnd  9026  axpownd  9033  axregnd  9036  axinfnd  9038  axacndlem5  9043  axacnd  9044  wl-ax11-lem1  31879  wl-ax11-lem3  31881  wl-ax11-lem9  31887  wl-ax11-lem10  31888  e2ebind  36900
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