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Theorem mtbid 630
Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 26-Nov-1995.)
Hypotheses
Ref Expression
mtbid.min  |-  ( ph  ->  -.  ps )
mtbid.maj  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
mtbid  |-  ( ph  ->  -.  ch )

Proof of Theorem mtbid
StepHypRef Expression
1 mtbid.min . 2  |-  ( ph  ->  -.  ps )
2 mtbid.maj . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
32biimprd 156 . 2  |-  ( ph  ->  ( ch  ->  ps ) )
41, 3mtod 622 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:  sylnib  634  eqneltrrd  2179  neleqtrd  2180  eueq3dc  2776  efrirr  4137  nqnq0pi  6726  zdclt  8542  frec2uzf1od  9524  expnegap0  9617  ibcval5  9823  rpdvds  10672  oddpwdclemodd  10741
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