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

Theorem imanim 778
Description: Express implication in terms of conjunction. The converse only holds given a decidability condition; see imandc 779. (Contributed by Jim Kingdon, 24-Dec-2017.)
Assertion
Ref Expression
imanim ((φψ) → ¬ (φ ¬ ψ))

Proof of Theorem imanim
StepHypRef Expression
1 annimim 775 . 2 ((φ ¬ ψ) → ¬ (φψ))
21con2i 545 1 ((φψ) → ¬ (φ ¬ ψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-in1 532  ax-in2 533
This theorem is referenced by:  difdif  3045  npss0  3242  ssdif0im  3262  inssdif0im  3267
  Copyright terms: Public domain W3C validator