Theorem pm3.43 592

Description: Theorem *3.43 (Comp) of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.) (Revised by NM, 27-Nov-2013.)

Assertion

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

Proof of Theorem pm3.43

Step	Hyp	Ref	Expression
1		pm3.43i 271	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜑 → 𝜒) → (𝜑 → (𝜓 ∧ 𝜒))))
2	1	imp 123	1 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → (𝜑 → (𝜓 ∧ 𝜒)))

Syntax hints:   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  jcab  593  sbequilem  1826  eqvinc  2849  eqvincg  2850