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Theorem pm3.31 442
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 → (𝜓𝜒)) → ((𝜑𝜓) → 𝜒))

Proof of Theorem pm3.31
StepHypRef Expression
1 id 22 . 2 ((𝜑 → (𝜓𝜒)) → (𝜑 → (𝜓𝜒)))
21impd 400 1 ((𝜑 → (𝜓𝜒)) → ((𝜑𝜓) → 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 386
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 199  df-an 387
This theorem is referenced by:  impexp  443  imp5aOLD  444  idrefOLD  5755  bj-sb56  33174  bj-ssbequ2  33178  trsbc  39579  3impexpVD  39905  trsbcVD  39926  19.41rgVD  39951  stoweidlem17  41022
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