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Theorem nalequcoms 1455
Description: A commutation rule for distinct variable specifiers. (Contributed by NM, 2-Jan-2002.) (Revised by Mario Carneiro, 2-Feb-2015.)
Hypothesis
Ref Expression
nalequcoms.1  |-  ( -. 
A. x  x  =  y  ->  ph )
Assertion
Ref Expression
nalequcoms  |-  ( -. 
A. y  y  =  x  ->  ph )

Proof of Theorem nalequcoms
StepHypRef Expression
1 alequcom 1453 . . 3  |-  ( A. x  x  =  y  ->  A. y  y  =  x )
21con3i 597 . 2  |-  ( -. 
A. y  y  =  x  ->  -.  A. x  x  =  y )
3 nalequcoms.1 . 2  |-  ( -. 
A. x  x  =  y  ->  ph )
42, 3syl 14 1  |-  ( -. 
A. y  y  =  x  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1287    = wceq 1289
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 579  ax-in2 580  ax-10 1441
This theorem is referenced by:  nd5  1746
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