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Theorem pm3.31 253
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 246 1 ((𝜑 → (𝜓𝜒)) → ((𝜑𝜓) → 𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104
This theorem is referenced by:  impexp  254  imp5a  344  equsexd  1633  mo3h  1969  rexim  2430  peano5  4349  issref  4735  bj-indind  10443  peano5setOLD  10452
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