Theorem imorri 869

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 867	. 2 ⊢ ((𝜑 → 𝜓) ↔ (¬ 𝜑 ∨ 𝜓))
3	1, 2	mpbir 234	1 ⊢ (𝜑 → 𝜓)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 861

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

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  anmp  1784  meran2  37200  meran3  37201