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 → 𝜓 ) ∧ ( 𝜒 → 𝜃 ) ) → ( ( 𝜑 ∨ 𝜒 ) → ( 𝜓 ∨ 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		simpl	⊢ ( ( ( 𝜑 → 𝜓 ) ∧ ( 𝜒 → 𝜃 ) ) → ( 𝜑 → 𝜓 ) )
2		simpr	⊢ ( ( ( 𝜑 → 𝜓 ) ∧ ( 𝜒 → 𝜃 ) ) → ( 𝜒 → 𝜃 ) )
3	1 2	orim12d	⊢ ( ( ( 𝜑 → 𝜓 ) ∧ ( 𝜒 → 𝜃 ) ) → ( ( 𝜑 ∨ 𝜒 ) → ( 𝜓 ∨ 𝜃 ) ) )