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Theorem naecoms-o 2250
Description: A commutation rule for distinct variable specifiers. Version of naecoms 2026 using ax-c11 2211. (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 2223 . . 3  |-  ( A. x  x  =  y  ->  A. y  y  =  x )
2 nalequcoms-o.1 . . 3  |-  ( -. 
A. x  x  =  y  ->  ph )
31, 2nsyl4 142 . 2  |-  ( -. 
ph  ->  A. y  y  =  x )
43con1i 129 1  |-  ( -. 
A. y  y  =  x  ->  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1377
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-c11 2211
This theorem depends on definitions:  df-bi 185  df-ex 1597
This theorem is referenced by:  ax12inda2ALT  2269
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