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Theorem mtbi 605
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 128 . 2 (𝜓𝜑)
41, 3mto 598 1 ¬ 𝜓
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  mtbir  606  vprc  3915  vnex  3917  onsucelsucexmid  4282  dtruex  4310  dmsn0  4815  php5  6351  bj-vprc  10375  bj-vnex  10377
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