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

Theorem intnanrd 852
Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 10-Jul-2005.)
Hypothesis
Ref Expression
intnand.1  |-  ( ph  ->  -.  ps )
Assertion
Ref Expression
intnanrd  |-  ( ph  ->  -.  ( ps  /\  ch ) )

Proof of Theorem intnanrd
StepHypRef Expression
1 intnand.1 . 2  |-  ( ph  ->  -.  ps )
2 simpl 106 . 2  |-  ( ( ps  /\  ch )  ->  ps )
31, 2nsyl 568 1  |-  ( ph  ->  -.  ( ps  /\  ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-in1 554  ax-in2 555
This theorem is referenced by:  dcan  853  bianfd  866  frecsuclem3  6021  xrrebnd  8833  fzpreddisj  9035
  Copyright terms: Public domain W3C validator