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Theorem aecoms-o 2104
Description: A commutation rule for identical variable specifiers. Version of aecoms 1900 using ax-10o . (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)
Hypothesis
Ref Expression
alequcoms-o.1  |-  ( A. x  x  =  y  ->  ph )
Assertion
Ref Expression
aecoms-o  |-  ( A. y  y  =  x  ->  ph )

Proof of Theorem aecoms-o
StepHypRef Expression
1 aecom-o 2103 . 2  |-  ( A. y  y  =  x  ->  A. x  x  =  y )
2 alequcoms-o.1 . 2  |-  ( A. x  x  =  y  ->  ph )
31, 2syl 15 1  |-  ( A. y  y  =  x  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530
This theorem is referenced by:  hbae-o  2105  dral1-o  2106  dvelimf-o  2132  aev-o  2134  ax11indalem  2149  ax11inda2ALT  2150
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-10o 2091
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