Metamath Proof Explorer

Theorem pm3.48ALT

Description: Alternate proof of pm3.48 . (Contributed by Hongxiu Chen, 29-Jun-2025) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	pm3.48ALT	$⊢ ((φ \to ψ) \land (χ \to θ)) \to ((φ \lor χ) \to (ψ \lor θ))$

Proof

Step	Hyp	Ref	Expression
1		simpl	$⊢ ((φ \to ψ) \land (χ \to θ)) \to (φ \to ψ)$
2		simpr	$⊢ ((φ \to ψ) \land (χ \to θ)) \to (χ \to θ)$
3	1 2	orim12d	$⊢ ((φ \to ψ) \land (χ \to θ)) \to ((φ \lor χ) \to (ψ \lor θ))$