Theorem pm3.43 610

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 273	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜑 → 𝜒) → (𝜑 → (𝜓 ∧ 𝜒))))
2	1	imp 124	1 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → (𝜑 → (𝜓 ∧ 𝜒)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is used by:  jcab  611  sbequilem  1891  eqvinc  2949  eqvincg  2950