Theorem imorri 403

Description: Infer implication from disjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)

Hypothesis

Ref	Expression
imorri.1	⊢ (¬ φ ∨ ψ)

Assertion

Ref	Expression
imorri	⊢ (φ → ψ)

Proof of Theorem imorri

Step	Hyp	Ref	Expression
1		imorri.1	. 2 ⊢ (¬ φ ∨ ψ)
2		imor 401	. 2 ⊢ ((φ → ψ) ↔ (¬ φ ∨ ψ))
3	1, 2	mpbir 200	1 ⊢ (φ → ψ)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is referenced by:  anmp  1516