Theorem pm3.43 478

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 477	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜑 → 𝜒) → (𝜑 → (𝜓 ∧ 𝜒))))
2	1	imp 411	1 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → (𝜑 → (𝜓 ∧ 𝜒)))

Syntax hints:   → wi 4   ∧ wa 400

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 210  df-an 401

This theorem is referenced by:  jcab  526  anim12ii  629  darapti  2711  eqvincg  3607  bnj1110  35370  bj-axreprepsep  37712  jm2.18  43715  jm2.15nn0  43730  jm2.16nn0  43731  cotrintab  44340