ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  hbnaes Unicode version

Theorem hbnaes 1723
Description: Rule that applies hbnae 1721 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 1721 . 2  |-  ( -. 
A. x  x  =  y  ->  A. z  -.  A. x  x  =  y )
2 hbnalequs.1 . 2  |-  ( A. z  -.  A. x  x  =  y  ->  ph )
31, 2syl 14 1  |-  ( -. 
A. x  x  =  y  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1351
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-fal 1359
This theorem is referenced by:  sbal2  2020
  Copyright terms: Public domain W3C validator