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Theorem con3 632
Description: Contraposition. Theorem *2.16 of [WhiteheadRussell] p. 103. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 13-Feb-2013.)
Assertion
Ref Expression
con3 ((𝜑𝜓) → (¬ 𝜓 → ¬ 𝜑))

Proof of Theorem con3
StepHypRef Expression
1 id 19 . 2 ((𝜑𝜓) → (𝜑𝜓))
21con3d 621 1 ((𝜑𝜓) → (¬ 𝜓 → ¬ 𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 604  ax-in2 605
This theorem is referenced by:  mtt  675  annimim  676  pm3.37  679  const  842  con34bdc  861  hbnt  1640  ralf0  3508  ltleletr  7972  ltnsym  7976  bj-nnsn  13468  bj-nnclavius  13472
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