Theorem imorr 711

Description: Implication in terms of disjunction. One direction of theorem *4.6 of [WhiteheadRussell] p. 120. The converse holds for decidable propositions, as seen at imordc 887. (Contributed by Jim Kingdon, 21-Jul-2018.)

Assertion

Ref	Expression
imorr	⊢ ((¬ 𝜑 ∨ 𝜓) → (𝜑 → 𝜓))

Proof of Theorem imorr

Step	Hyp	Ref	Expression
1		ax-in2 605	. 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))
2		ax-1 6	. 2 ⊢ (𝜓 → (𝜑 → 𝜓))
3	1, 2	jaoi 706	1 ⊢ ((¬ 𝜑 ∨ 𝜓) → (𝜑 → 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 698

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 605  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm4.52im  740  nf4r  1658