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

Theorem imnani 658
Description: Express implication in terms of conjunction. (Contributed by Mario Carneiro, 28-Sep-2015.)
Hypothesis
Ref Expression
imnani.1  |-  -.  ( ph  /\  ps )
Assertion
Ref Expression
imnani  |-  ( ph  ->  -.  ps )

Proof of Theorem imnani
StepHypRef Expression
1 imnani.1 . 2  |-  -.  ( ph  /\  ps )
2 imnan 657 . 2  |-  ( (
ph  ->  -.  ps )  <->  -.  ( ph  /\  ps ) )
31, 2mpbir 144 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  mptnan  1355  eueq3dc  2767  dtruex  4310  nntri2  6138  nndcel  6144
  Copyright terms: Public domain W3C validator