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Theorem con2b 324
Description: Contraposition. Bidirectional version of con2 108. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
con2b ((φ → ¬ ψ) ↔ (ψ → ¬ φ))

Proof of Theorem con2b
StepHypRef Expression
1 con2 108 . 2 ((φ → ¬ ψ) → (ψ → ¬ φ))
2 con2 108 . 2 ((ψ → ¬ φ) → (φ → ¬ ψ))
31, 2impbii 180 1 ((φ → ¬ ψ) ↔ (ψ → ¬ φ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177
This theorem is referenced by:  mt2bi  328  pm4.15  564  nic-ax  1438  nic-axALT  1439  ssconb  3399  disjsn  3786  evenodddisj  4516
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