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Theorem naecoms 2003
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 1991 . . 3  |-  ( A. x  x  =  y  ->  A. y  y  =  x )
2 naecoms.1 . . 3  |-  ( -. 
A. x  x  =  y  ->  ph )
31, 2nsyl4 136 . 2  |-  ( -. 
ph  ->  A. y  y  =  x )
43con1i 123 1  |-  ( -. 
A. y  y  =  x  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1546
This theorem is referenced by:  eujustALT  2265  nfcvf2  2571
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551
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