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Theorem pm3.3 452
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 419 1 (((𝜑𝜓) → 𝜒) → (𝜑 → (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399
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 400
This theorem is referenced by:  impexp  454  pm4.79  1003  trer  34135  bj-alanim  34421  wl-mo3t  35343  trsbc  41682  simplbi2VD  41988  exbirVD  41995  exbiriVD  41996  3impexpVD  41998  trsbcVD  42019  simplbi2comtVD  42030
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