Theorem ori 364

Description: Infer implication from disjunction. (Contributed by NM, 11-Jun-1994.)

Hypothesis

Ref	Expression
ori.1	⊢ (φ ∨ ψ)

Assertion

Ref	Expression
ori	⊢ (¬ φ → ψ)

Proof of Theorem ori

Step	Hyp	Ref	Expression
1		ori.1	. 2 ⊢ (φ ∨ ψ)
2		df-or 359	. 2 ⊢ ((φ ∨ ψ) ↔ (¬ φ → ψ))
3	1, 2	mpbi 199	1 ⊢ (¬ φ → ψ)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by:  3ori  1242  mtp-or  1538  moexex  2273  mo2icl  3016  mosubopt  4613