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Theorem mtbi 630
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 623 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 579  ax-in2 580
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  mtbir  631  vnex  3962  onsucelsucexmid  4336  dtruex  4365  dmsn0  4885  php5  6554  ndvdsi  11015  nprmi  11188  unennn  11292  bj-vprc  11433  bj-vnex  11435
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