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Theorem naecoms 2146
Description: A commutation rule for distinct variable specifiers. (Contributed by NM, 2-Jan-2002.)
Hypothesis
Ref Expression
naecoms.1  |-  ( -. 
A. x  x  =  y  ->  ph )
Assertion
Ref Expression
naecoms  |-  ( -. 
A. y  y  =  x  ->  ph )

Proof of Theorem naecoms
StepHypRef Expression
1 aecom 2144 . 2  |-  ( A. x  x  =  y  <->  A. y  y  =  x )
2 naecoms.1 . 2  |-  ( -. 
A. x  x  =  y  ->  ph )
31, 2sylnbir 309 1  |-  ( -. 
A. y  y  =  x  ->  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1441
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-12 1932  ax-13 2090
This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1663  df-nf 1667
This theorem is referenced by:  sb9  2254  eujustALT  2301  nfcvf2  2615  axpowndlem2  9020  wl-sbcom2d  31884  wl-mo2df  31892  wl-eudf  31894
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