Theorem imorri 706

Description: Infer implication from disjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Revised by Mario Carneiro, 31-Jan-2015.)

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		pm2.21 585	. . 3 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))
3		ax-1 5	. . 3 ⊢ (𝜓 → (𝜑 → 𝜓))
4	2, 3	jaoi 674	. 2 ⊢ ((¬ 𝜑 ∨ 𝜓) → (𝜑 → 𝜓))
5	1, 4	ax-mp 7	1 ⊢ (𝜑 → 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 667

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 583  ax-io 668

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)