Theorem pm4.77 762

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 758	. 2 ⊢ (((ψ ∨ χ) → φ) ↔ ((ψ → φ) ∧ (χ → φ)))
2	1	bicomi 193	1 ⊢ (((ψ → φ) ∧ (χ → φ)) ↔ ((ψ ∨ χ) → φ))

Syntax hints:   → wi 4   ↔ wb 176   ∨ wo 357   ∧ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is referenced by: (None)