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Theorem con2b 626
Description: Contraposition. Bidirectional version of con2 605. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
con2b ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))

Proof of Theorem con2b
StepHypRef Expression
1 con2 605 . 2 ((𝜑 → ¬ 𝜓) → (𝜓 → ¬ 𝜑))
2 con2 605 . 2 ((𝜓 → ¬ 𝜑) → (𝜑 → ¬ 𝜓))
31, 2impbii 124 1 ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  mt2bi  642  pm4.15  823  dfdif3  3094  ssconb  3117  disjsn  3478  isprm3  10880
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