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Theorem mtt 609
Description: Modus-tollens-like theorem. (Contributed by NM, 7-Apr-2001.) (Revised by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
mtt φ → (¬ ψ ↔ (ψφ)))

Proof of Theorem mtt
StepHypRef Expression
1 pm2.21 547 . 2 ψ → (ψφ))
2 con3 570 . . 3 ((ψφ) → (¬ φ → ¬ ψ))
32com12 27 . 2 φ → ((ψφ) → ¬ ψ))
41, 3impbid2 131 1 φ → (¬ ψ ↔ (ψφ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  nbn2  612  dfnot  1261
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