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Theorem hbnae-o 2131
Description: All variables are effectively bound in a distinct variable specifier. Lemma L19 in [Megill] p. 446 (p. 14 of the preprint). Version of hbnae 1908 using ax-10o 2091. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
hbnae-o  |-  ( -. 
A. x  x  =  y  ->  A. z  -.  A. x  x  =  y )

Proof of Theorem hbnae-o
StepHypRef Expression
1 hbae-o 2105 . 2  |-  ( A. x  x  =  y  ->  A. z A. x  x  =  y )
21hbn 1732 1  |-  ( -. 
A. x  x  =  y  ->  A. z  -.  A. x  x  =  y )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530
This theorem is referenced by:  dvelimf-o  2132  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-6 1715  ax-7 1720  ax-11 1727  ax-4 2087  ax-5o 2088  ax-6o 2089  ax-10o 2091  ax-12o 2094
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