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

Theorem imanim 823
Description: Express implication in terms of conjunction. The converse only holds given a decidability condition; see imandc 824. (Contributed by Jim Kingdon, 24-Dec-2017.)
Assertion
Ref Expression
imanim  |-  ( (
ph  ->  ps )  ->  -.  ( ph  /\  -.  ps ) )

Proof of Theorem imanim
StepHypRef Expression
1 annimim 820 . 2  |-  ( (
ph  /\  -.  ps )  ->  -.  ( ph  ->  ps ) )
21con2i 592 1  |-  ( (
ph  ->  ps )  ->  -.  ( 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-in1 579  ax-in2 580
This theorem is referenced by:  difdif  3125  ssdif0im  3347  inssdif0im  3350  nominpos  8651
  Copyright terms: Public domain W3C validator