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Theorem pm3.31 260
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 252 1 ((𝜑 → (𝜓𝜒)) → ((𝜑𝜓) → 𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106
This theorem is referenced by:  impexp  261  imp5a  356  equsexd  1722  mo3h  2072  rexim  2564  peano5  4580  issref  4991  bj-indind  13927
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