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Theorem con3 643
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 632 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 615  ax-in2 616
This theorem is referenced by:  mtt  686  annimim  687  pm3.37  690  con34bdc  872  hbnt  1663  ralf0  3538  ltleletr  8053  ltnsym  8057  bj-nnsn  14838  bj-nnclavius  14842  bj-con1st  14856
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