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Theorem hbnae-o 1845
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 1844 using ax-10o 1835. (Contributed by NM, 5-Aug-1993.)
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 1841 . 2  |-  ( A. x  x  =  y  ->  A. z A. x  x  =  y )
21hbn 1722 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 1532
This theorem is referenced by:  dvelimf-o  1854  ax11indalem  2110  ax11inda2ALT  2111
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-12o 1664  ax-9 1684  ax-4 1692  ax-10o 1835
This theorem depends on definitions:  df-bi 179  df-nf 1540
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