Theorem pm4.77 799

Description: Theorem *4.77 of [WhiteheadRussell] p. 121. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.77	⊢ (((𝜓 → 𝜑) ∧ (𝜒 → 𝜑)) ↔ ((𝜓 ∨ 𝜒) → 𝜑))

Proof of Theorem pm4.77

Step	Hyp	Ref	Expression
1		jaob 710	. 2 ⊢ (((𝜓 ∨ 𝜒) → 𝜑) ↔ ((𝜓 → 𝜑) ∧ (𝜒 → 𝜑)))
2	1	bicomi 132	1 ⊢ (((𝜓 → 𝜑) ∧ (𝜒 → 𝜑)) ↔ ((𝜓 ∨ 𝜒) → 𝜑))

Syntax hints:   → wi 4   ∧ wa 104   ↔ wb 105   ∨ wo 708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)