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Theorem pm3.31 461
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 447 1 ((𝜑 → (𝜓𝜒)) → ((𝜑𝜓) → 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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 386
This theorem is referenced by:  impexp  462  imp5a  623  issref  5468  bj-sb56  32281  bj-ssbequ2  32285  trsbc  38232  3impexpVD  38574  trsbcVD  38596  19.41rgVD  38621  stoweidlem17  39541
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