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Theorem mtbii 632
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 156 . 2  |-  ( ph  ->  ( ch  ->  ps ) )
41, 3mtoi 623 1  |-  ( ph  ->  -.  ch )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  onsucelsucexmid  4301  nntri2  6158  nntri3  6161  nndceq  6163  inffiexmid  6457  genpdisj  6827  ltposr  7054  hashennn  9856
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