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Theorem naecoms 2041
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 ax10 2029 . . 3  |-  ( A. x  x  =  y  ->  A. y  y  =  x )
2 naecoms.1 . . 3  |-  ( -. 
A. x  x  =  y  ->  ph )
31, 2nsyl4 137 . 2  |-  ( -. 
ph  ->  A. y  y  =  x )
43con1i 124 1  |-  ( -. 
A. y  y  =  x  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1550
This theorem is referenced by:  eujustALT  2291  nfcvf2  2602
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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