Theorem pm3.43i 442

Description: Nested conjunction of antecedents. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem pm3.43i

Step	Hyp	Ref	Expression
1		pm3.2 434	. 2 ⊢ (ψ → (χ → (ψ ∧ χ)))
2	1	imim3i 55	1 ⊢ ((φ → ψ) → ((φ → χ) → (φ → (ψ ∧ χ))))

Syntax hints:   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by:  pm3.43  832