Metamath Proof Explorer

Theorem jao

Description: Disjunction of antecedents. Compare Theorem *3.44 of WhiteheadRussell p. 113. (Contributed by NM, 5-Apr-1994) (Proof shortened by Wolf Lammen, 4-Apr-2013)

		Ref	Expression
	Assertion	jao	$⊢ (φ \to ψ) \to ((χ \to ψ) \to ((φ \lor χ) \to ψ))$

Proof

Step	Hyp	Ref	Expression
1		pm3.44	$⊢ ((φ \to ψ) \land (χ \to ψ)) \to ((φ \lor χ) \to ψ)$
2	1	ex	$⊢ (φ \to ψ) \to ((χ \to ψ) \to ((φ \lor χ) \to ψ))$