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Theorem con2b 348
Description: Contraposition. Bidirectional version of con2 130. (Contributed by NM, 12-Mar-1993.)
Assertion
Ref Expression
con2b ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))

Proof of Theorem con2b
StepHypRef Expression
1 con2 130 . 2 ((𝜑 → ¬ 𝜓) → (𝜓 → ¬ 𝜑))
2 con2 130 . 2 ((𝜓 → ¬ 𝜑) → (𝜑 → ¬ 𝜓))
31, 2impbii 199 1 ((𝜑 → ¬ 𝜓) ↔ (𝜓 → ¬ 𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196
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 197
This theorem is referenced by:  mt2bi  352  pm4.15  604  nic-ax  1638  nic-axALT  1639  alimex  1798  ssconb  3776  disjsn  4278  oneqmini  5814  kmlem4  9013  isprm3  15443  bnj1171  31194  bnj1176  31199  bnj1204  31206  bnj1388  31227  bnj1523  31265  wl-nancom  33427  dfxor5  38376  pm13.196a  38932
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