Theorem pm3.48ALT 36186

Description: Alternate proof of pm3.48 977. (Contributed by Hongxiu Chen, 29-Jun-2025.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
pm3.48ALT	⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜃)) → ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜃)))

Proof of Theorem pm3.48ALT

Step	Hyp	Ref	Expression
1		simpl 487	. 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜃)) → (𝜑 → 𝜓))
2		simpr 489	. 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜃)) → (𝜒 → 𝜃))
3	1, 2	orim12d 978	1 ⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜃)) → ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜃)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 400   ∨ wo 860

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861

This theorem is used by: (None)