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

Theorem orcanai 848
Description: Change disjunction in consequent to conjunction in antecedent. (Contributed by NM, 8-Jun-1994.)
Hypothesis
Ref Expression
orcanai.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
orcanai ((𝜑 ∧ ¬ 𝜓) → 𝜒)

Proof of Theorem orcanai
StepHypRef Expression
1 orcanai.1 . . 3 (𝜑 → (𝜓𝜒))
21ord 653 . 2 (𝜑 → (¬ 𝜓𝜒))
32imp 119 1 ((𝜑 ∧ ¬ 𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 101  wo 639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in2 555  ax-io 640
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator