Theorem pm3.44

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

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

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ( 𝜓 → 𝜑 ) → ( 𝜓 → 𝜑 ) )
2		id	⊢ ( ( 𝜒 → 𝜑 ) → ( 𝜒 → 𝜑 ) )
3	1 2	jaao	⊢ ( ( ( 𝜓 → 𝜑 ) ∧ ( 𝜒 → 𝜑 ) ) → ( ( 𝜓 ∨ 𝜒 ) → 𝜑 ) )