MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  hbnae Unicode version

Theorem hbnae 1844
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 1840 . 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:  hbnaes  1847  dvelimfALT  1853  eujustALT  2117  a9e2nd  27017  a9e2ndVD  27374  a9e2ndeqVD  27375  a9e2ndALT  27397  a9e2ndeqALT  27398  ax12-2  27792
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-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
  Copyright terms: Public domain W3C validator