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Theorem hbnae 2009
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 2006 . 2  |-  ( A. x  x  =  y  ->  A. z A. x  x  =  y )
21hbn 1797 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 1546
This theorem is referenced by:  hbnaes  2011  dvelimhOLD  2018  eujustALT  2261  a9e2nd  28360  a9e2ndVD  28733  a9e2ndeqVD  28734  a9e2ndALT  28756  a9e2ndeqALT  28757
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551
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