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Theorem con2b 659
Description: Contraposition. Bidirectional version of con2 633. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
con2b ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))

Proof of Theorem con2b
StepHypRef Expression
1 con2 633 . 2 ((𝜑 → ¬ 𝜓) → (𝜓 → ¬ 𝜑))
2 con2 633 . 2 ((𝜓 → ¬ 𝜑) → (𝜑 → ¬ 𝜓))
31, 2impbii 125 1 ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  mt2bi  674  pm4.15  684  dfdif3  3187  ssconb  3210  disjsn  3589  isprm3  11826
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