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Theorem hbnae-o 2120
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 1897 using ax-10o 2081. (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 2094 . 2  |-  ( A. x  x  =  y  ->  A. z A. x  x  =  y )
21hbn 1721 1  |-  ( -. 
A. x  x  =  y  ->  A. z  -.  A. x  x  =  y )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6   A.wal 1528
This theorem is referenced by:  dvelimf-o  2121  ax11indalem  2137  ax11inda2ALT  2138
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-6 1704  ax-7 1709  ax-11 1716  ax-4 2077  ax-5o 2078  ax-6o 2079  ax-10o 2081  ax-12o 2084
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