Theorem pm4.77

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

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

Proof

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