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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  |-  -.  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 128 . 2  |-  ( ps 
->  ph )
41, 3mto 598 1  |-  -.  ps
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  3916  vnex  3918  onsucelsucexmid  4283  dtruex  4311  dmsn0  4816  php5  6352  ndvdsi  10245  bj-vprc  10403  bj-vnex  10405
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