Theorem pm3.43i 478

Description: Nested conjunction of antecedents. (Contributed by NM, 4-Jan-1993.)

Assertion

Ref	Expression
pm3.43i	⊢ ((𝜑 → 𝜓) → ((𝜑 → 𝜒) → (𝜑 → (𝜓 ∧ 𝜒))))

Proof of Theorem pm3.43i

Step	Hyp	Ref	Expression
1		pm3.2 475	. 2 ⊢ (𝜓 → (𝜒 → (𝜓 ∧ 𝜒)))
2	1	imim3i 65	1 ⊢ ((𝜑 → 𝜓) → ((𝜑 → 𝜒) → (𝜑 → (𝜓 ∧ 𝜒))))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

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 402

This theorem is used by:  pm3.43  479  bnj1110  35402