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Theorem mtbi 582
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 124 . 2 (ψφ)
41, 3mto 575 1 ¬ ψ
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  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 532  ax-in2 533
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  mtbir  583  vprc  3862  vnex  3864  onsucelsucexmid  4199  dtruex  4221  dmsn0  4715  bj-vprc  7266  bj-vnex  7268
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