Theorem pm3.43 479

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 478	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜑 → 𝜒) → (𝜑 → (𝜓 ∧ 𝜒))))
2	1	imp 412	1 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → (𝜑 → (𝜓 ∧ 𝜒)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  jcab  527  anim12ii  630  darapti  2713  eqvincg  3609  bnj1110  35411  bj-axreprepsep  37745  jm2.18  43748  jm2.15nn0  43763  jm2.16nn0  43764  cotrintab  44373