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

Theorem orcanai 825
Description: Change disjunction in consequent to conjunction in antecedent. (Contributed by NM, 8-Jun-1994.)
Hypothesis
Ref Expression
orcanai.1 (φ → (ψ χ))
Assertion
Ref Expression
orcanai ((φ ¬ ψ) → χ)

Proof of Theorem orcanai
StepHypRef Expression
1 orcanai.1 . . 3 (φ → (ψ χ))
21ord 630 . 2 (φ → (¬ ψχ))
32imp 115 1 ((φ ¬ ψ) → χ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97   wo 616
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 533  ax-io 617
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator