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Theorem mtoi 577
Description: Modus tollens inference. (Contributed by NM, 5-Jul-1994.) (Proof shortened by Wolf Lammen, 15-Sep-2012.)
Hypotheses
Ref Expression
mtoi.1 ¬ χ
mtoi.2 (φ → (ψχ))
Assertion
Ref Expression
mtoi (φ → ¬ ψ)

Proof of Theorem mtoi
StepHypRef Expression
1 mtoi.1 . . 3 ¬ χ
21a1i 9 . 2 (φ → ¬ χ)
3 mtoi.2 . 2 (φ → (ψχ))
42, 3mtod 576 1 (φ → ¬ ψ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 532  ax-in2 533
This theorem is referenced by:  mtbii  586  mtbiri  587  pwnss  3886  nsuceq0g  4104  ordsuc  4225  onnmin  4228  ssnel  4229  onpsssuc  4231  acexmidlemab  5430  reldmtpos  5790  dmtpos  5793  2pwuninelg  5820  ltexprlemdisj  6443  recexprlemdisj  6464
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