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Theorem mtbii 663
Description: An inference from a biconditional, similar to modus tollens. (Contributed by NM, 27-Nov-1995.)
Hypotheses
Ref Expression
mtbii.min  |-  -.  ps
mtbii.maj  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
mtbii  |-  ( ph  ->  -.  ch )

Proof of Theorem mtbii
StepHypRef Expression
1 mtbii.min . 2  |-  -.  ps
2 mtbii.maj . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
32biimprd 157 . 2  |-  ( ph  ->  ( ch  ->  ps ) )
41, 3mtoi 653 1  |-  ( ph  ->  -.  ch )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> 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 603  ax-in2 604
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  onsucelsucexmid  4445  nntri2  6390  nntri3  6393  nndceq  6395  inffiexmid  6800  genpdisj  7338  ltposr  7578  hashennn  10533  fsumsplit  11183  sumsplitdc  11208
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