Theorem pm3.31 450

Description: Theorem *3.31 (Imp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)

Assertion

Ref	Expression
pm3.31	⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 ∧ 𝜓) → 𝜒))

Proof of Theorem pm3.31

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (𝜓 → 𝜒)))
2	1	impd 411	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 ∧ 𝜓) → 𝜒))

Syntax hints:   → wi 4   ∧ wa 396

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 206  df-an 397

This theorem is referenced by:  impexp  451  bj-subst  34842  trsbc  42160  3impexpVD  42476  trsbcVD  42497  19.41rgVD  42522  stoweidlem17  43558