Theorem pm3.3 453

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 23	. 2 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) → ((𝜑 ∧ 𝜓) → 𝜒))
2	1	expd 420	1 ⊢ (((𝜑 ∧ 𝜓) → 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:  impexp  455  pm4.79  1019  trer  36684  bj-alanim  37077  wl-mo3t  38086  trsbc  45108  simplbi2VD  45413  exbirVD  45420  exbiriVD  45421  3impexpVD  45423  trsbcVD  45444  simplbi2comtVD  45455