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Theorem mtbi 628
Description: An inference from a biconditional, related to modus tollens. (Contributed by NM, 15-Nov-1994.) (Proof shortened by Wolf Lammen, 25-Oct-2012.)
Hypotheses
Ref Expression
mtbi.1 ¬ 𝜑
mtbi.2 (𝜑𝜓)
Assertion
Ref Expression
mtbi ¬ 𝜓

Proof of Theorem mtbi
StepHypRef Expression
1 mtbi.1 . 2 ¬ 𝜑
2 mtbi.2 . . 3 (𝜑𝜓)
32biimpri 131 . 2 (𝜓𝜑)
41, 3mto 621 1 ¬ 𝜓
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  mtbir  629  vnex  3938  onsucelsucexmid  4312  dtruex  4341  dmsn0  4855  php5  6507  ndvdsi  10727  nprmi  10900  unennn  11004  bj-vprc  11144  bj-vnex  11146
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