Theorem pm3.44 704

Description: Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 3-Oct-2013.)

Assertion

Ref	Expression
pm3.44	⊢ (((𝜓 → 𝜑) ∧ (𝜒 → 𝜑)) → ((𝜓 ∨ 𝜒) → 𝜑))

Proof of Theorem pm3.44

Step	Hyp	Ref	Expression
1		jaob 699	. 2 ⊢ (((𝜓 ∨ 𝜒) → 𝜑) ↔ ((𝜓 → 𝜑) ∧ (𝜒 → 𝜑)))
2	1	biimpri 132	1 ⊢ (((𝜓 → 𝜑) ∧ (𝜒 → 𝜑)) → ((𝜓 ∨ 𝜒) → 𝜑))

Syntax hints:   → wi 4   ∧ wa 103   ∨ wo 697

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-io 698

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  jaoi  705  jao  744  pm2.6dc  847  pm4.83dc  935