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Theorem mtbi 642
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  |-  -.  ph
mtbi.2  |-  ( ph  <->  ps )
Assertion
Ref Expression
mtbi  |-  -.  ps

Proof of Theorem mtbi
StepHypRef Expression
1 mtbi.1 . 2  |-  -.  ph
2 mtbi.2 . . 3  |-  ( ph  <->  ps )
32biimpri 132 . 2  |-  ( ps 
->  ph )
41, 3mto 634 1  |-  -.  ps
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  mtbir  643  vnex  4027  onsucelsucexmid  4413  dtruex  4442  dmsn0  4974  php5  6718  ndvdsi  11537  nprmi  11712  unennn  11816  bj-vprc  12928  bj-vnex  12930
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