Theorem pm3.43 832

Description: Theorem *3.43 (Comp) of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.)

Assertion

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

Proof of Theorem pm3.43

Step	Hyp	Ref	Expression
1		pm3.43i 442	. 2 ⊢ ((φ → ψ) → ((φ → χ) → (φ → (ψ ∧ χ))))
2	1	imp 418	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:  jcab  833  eqvinc  2967