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Theorem mtbi 671
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 133 . 2  |-  ( ps 
->  ph )
41, 3mto 663 1  |-  -.  ps
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  mtbir  672  vnex  4149  onsucelsucexmid  4547  dtruex  4576  dmsn0  5114  php5  6886  exmidonfinlem  7222  ndvdsi  11970  nprmi  12156  unennn  12448  bj-vprc  15106  bj-vnex  15108  trirec0xor  15252
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