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Theorem hbnae 1897
Description: All variables are effectively bound in a distinct variable specifier. Lemma L19 in [Megill] p. 446 (p. 14 of the preprint). (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
hbnae  |-  ( -. 
A. x  x  =  y  ->  A. z  -.  A. x  x  =  y )

Proof of Theorem hbnae
StepHypRef Expression
1 hbae 1895 . 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 3    -> wi 4   A.wal 1529
This theorem is referenced by:  hbnaes  1899  dvelimh  1906  eujustALT  2148  a9e2nd  28380  a9e2ndVD  28757  a9e2ndeqVD  28758  a9e2ndALT  28780  a9e2ndeqALT  28781  ax12-2  29176
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1531  df-nf 1534
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