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Theorem pm3.31 258
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 19 . 2 ((𝜑 → (𝜓𝜒)) → (𝜑 → (𝜓𝜒)))
21impd 251 1 ((𝜑 → (𝜓𝜒)) → ((𝜑𝜓) → 𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem is referenced by:  impexp  259  imp5a  350  equsexd  1664  mo3h  2001  rexim  2467  peano5  4413  issref  4814  bj-indind  11827
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