Theorem pm3.43i 473

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		pm3.2 470	. 2 ⊢ (𝜓 → (𝜒 → (𝜓 ∧ 𝜒)))
2	1	imim3i 64	1 ⊢ ((𝜑 → 𝜓) → ((𝜑 → 𝜒) → (𝜑 → (𝜓 ∧ 𝜒))))

Syntax hints:   → wi 4   ∧ wa 396

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397

This theorem is referenced by:  pm3.43  474  bnj1110  32962