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Theorem con1 141
Description: Contraposition. Theorem *2.15 of [WhiteheadRussell] p. 102. Its associated inference is con1i 142. (Contributed by NM, 29-Dec-1992.) (Proof shortened by Wolf Lammen, 12-Feb-2013.)
Assertion
Ref Expression
con1 ((¬ 𝜑𝜓) → (¬ 𝜓𝜑))

Proof of Theorem con1
StepHypRef Expression
1 id 22 . 2 ((¬ 𝜑𝜓) → (¬ 𝜑𝜓))
21con1d 137 1 ((¬ 𝜑𝜓) → (¬ 𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  con1b  346  nneob  7596  uzwo  11585
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