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Theorem pm3.3 459
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 (((𝜑𝜓) → 𝜒) → (𝜑 → (𝜓𝜒)))

Proof of Theorem pm3.3
StepHypRef Expression
1 id 22 . 2 (((𝜑𝜓) → 𝜒) → ((𝜑𝜓) → 𝜒))
21expd 451 1 (((𝜑𝜓) → 𝜒) → (𝜑 → (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383
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 197  df-an 385
This theorem is referenced by:  impexp  461  pm4.79  606  trer  32435  bj-alanim  32721  bj-mo3OLD  32957  wl-mo3t  33488  trsbc  39067  simplbi2VD  39395  exbirVD  39402  exbiriVD  39403  3impexpVD  39405  trsbcVD  39427  simplbi2comtVD  39438
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