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Theorem mt4d 130
Description: Modus tollens deduction. (Contributed by NM, 9-Jun-2006.)
Hypotheses
Ref Expression
mt4d.1  |-  ( ph  ->  ps )
mt4d.2  |-  ( ph  ->  ( -.  ch  ->  -. 
ps ) )
Assertion
Ref Expression
mt4d  |-  ( ph  ->  ch )

Proof of Theorem mt4d
StepHypRef Expression
1 mt4d.1 . 2  |-  ( ph  ->  ps )
2 mt4d.2 . . 3  |-  ( ph  ->  ( -.  ch  ->  -. 
ps ) )
32con4d 97 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
41, 3mpd 14 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  mt4i  131  fin1a2s  8040  gchinf  8279  pwfseqlem4  8284  isprm2lem  12765  pcfac  12947  prmreclem3  12965  sylow1lem1  14909  irredrmul  15489  ioorcl2  18927  itg2gt0  19115  mdegmullem  19464  atom1d  22933  notnot2ALT  28292
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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