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Theorem naecoms-o 2117
Description: A commutation rule for distinct variable specifiers. Version of naecoms 1888 using ax-10o 2078. (Contributed by NM, 2-Jan-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nalequcoms-o.1  |-  ( -. 
A. x  x  =  y  ->  ph )
Assertion
Ref Expression
naecoms-o  |-  ( -. 
A. y  y  =  x  ->  ph )

Proof of Theorem naecoms-o
StepHypRef Expression
1 aecom-o 2090 . . 3  |-  ( A. x  x  =  y  ->  A. y  y  =  x )
2 nalequcoms-o.1 . . 3  |-  ( -. 
A. x  x  =  y  ->  ph )
31, 2nsyl4 134 . 2  |-  ( -. 
ph  ->  A. y  y  =  x )
43con1i 121 1  |-  ( -. 
A. y  y  =  x  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527
This theorem is referenced by:  ax11inda2ALT  2137
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-10o 2078
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