Theorem pm3.3 449

Description: Theorem *3.3 (Exp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)

Assertion

Ref	Expression
pm3.3	⊢ (((𝜑 ∧ 𝜓) → 𝜒) → (𝜑 → (𝜓 → 𝜒)))

Proof of Theorem pm3.3

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) → ((𝜑 ∧ 𝜓) → 𝜒))
2	1	expd 416	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  pm4.79  1001  trer  34505  bj-alanim  34794  wl-mo3t  35731  trsbc  42160  simplbi2VD  42466  exbirVD  42473  exbiriVD  42474  3impexpVD  42476  trsbcVD  42497  simplbi2comtVD  42508