Theorem jao 672

Description: Disjunction of antecedents. Compare Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 5-Apr-1994.) (Proof shortened by Wolf Lammen, 4-Apr-2013.)

Assertion

Ref	Expression
jao	⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜓) → ((𝜑 ∨ 𝜒) → 𝜓)))

Proof of Theorem jao

Step	Hyp	Ref	Expression
1		pm3.44 635	. 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)) → ((𝜑 ∨ 𝜒) → 𝜓))
2	1	ex 108	1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜓) → ((𝜑 ∨ 𝜒) → 𝜓)))

Syntax hints:   → wi 4   ∨ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  3jao  1196  suctr  4158