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

Theorem hbnaes 1897
Description: Rule that applies hbnae 1895 to antecedent. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
hbnalequs.1  |-  ( A. z  -.  A. x  x  =  y  ->  ph )
Assertion
Ref Expression
hbnaes  |-  ( -. 
A. x  x  =  y  ->  ph )

Proof of Theorem hbnaes
StepHypRef Expression
1 hbnae 1895 . 2  |-  ( -. 
A. x  x  =  y  ->  A. z  -.  A. x  x  =  y )
2 hbnalequs.1 . 2  |-  ( A. z  -.  A. x  x  =  y  ->  ph )
31, 2syl 15 1  |-  ( -. 
A. x  x  =  y  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527
This theorem is referenced by:  sbal1  2065
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532
  Copyright terms: Public domain W3C validator