Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  ecase23d Structured version   GIF version

Theorem ecase23d 1225
 Description: Variation of ecased 1224 with three disjuncts instead of two. (Contributed by NM, 22-Apr-1994.) (Revised by Jim Kingdon, 9-Dec-2017.)
Hypotheses
Ref Expression
ecase23d.1 (φ → ¬ χ)
ecase23d.2 (φ → ¬ θ)
ecase23d.3 (φ → (ψ χ θ))
Assertion
Ref Expression
ecase23d (φψ)

Proof of Theorem ecase23d
StepHypRef Expression
1 ecase23d.1 . 2 (φ → ¬ χ)
2 ecase23d.2 . . 3 (φ → ¬ θ)
3 ecase23d.3 . . . 4 (φ → (ψ χ θ))
4 df-3or 874 . . . 4 ((ψ χ θ) ↔ ((ψ χ) θ))
53, 4sylib 127 . . 3 (φ → ((ψ χ) θ))
62, 5ecased 1224 . 2 (φ → (ψ χ))
71, 6ecased 1224 1 (φψ)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 616   ∨ w3o 872 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  df-3or 874 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator