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Theorem hbnae-o 32412
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 2110 using ax-c11 32372. (Contributed by NM, 13-May-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 32386 . 2  |-  ( A. x  x  =  y  ->  A. z A. x  x  =  y )
21hbn 1949 1  |-  ( -. 
A. x  x  =  y  ->  A. z  -.  A. x  x  =  y )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-c5 32368  ax-c4 32369  ax-c7 32370  ax-c11 32372  ax-c9 32375
This theorem depends on definitions:  df-bi 188  df-ex 1660
This theorem is referenced by:  dvelimf-o  32413  ax12indalem  32429  ax12inda2ALT  32430
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