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Theorem mtbir 574
Description: An inference from a biconditional, related to modus tollens. (Contributed by NM, 15-Nov-1994.) (Proof shortened by Wolf Lammen, 14-Oct-2012.)
Hypotheses
Ref Expression
mtbir.1 ¬ ψ
mtbir.2 (φψ)
Assertion
Ref Expression
mtbir ¬ φ

Proof of Theorem mtbir
StepHypRef Expression
1 mtbir.1 . 2 ¬ ψ
2 mtbir.2 . . 3 (φψ)
32bicomi 121 . 2 (ψφ)
41, 3mtbi 573 1 ¬ φ
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 96
This theorem is referenced by:  fal  1204  ax-9  1354
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 97  ax-ia2 98  ax-ia3 99  ax-in1 526  ax-in2 527
This theorem depends on definitions:  df-bi 108
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