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Theorem mtt 355
Description: Modus-tollens-like theorem. (Contributed by NM, 7-Apr-2001.) (Proof shortened by Wolf Lammen, 12-Nov-2012.)
Assertion
Ref Expression
mtt 𝜑 → (¬ 𝜓 ↔ (𝜓𝜑)))

Proof of Theorem mtt
StepHypRef Expression
1 biimt 351 . 2 𝜑 → (¬ 𝜓 ↔ (¬ 𝜑 → ¬ 𝜓)))
2 con34b 307 . 2 ((𝜓𝜑) ↔ (¬ 𝜑 → ¬ 𝜓))
31, 2syl6bbr 280 1 𝜑 → (¬ 𝜓 ↔ (𝜓𝜑)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 197
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 198
This theorem is referenced by:  imnot  356  dfnot  1657  ralf0  4269  fnsuppres  7554  axpownd  9705  largei  29451
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