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Theorem mt4d 132
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 99 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
41, 3mpd 15 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  mt4i  133  fin1a2s  8220  gchinf  8458  pwfseqlem4  8463  isprm2lem  13006  pcfac  13188  prmreclem3  13206  sylow1lem1  15152  irredrmul  15732  ioorcl2  19324  itg2gt0  19512  mdegmullem  19861  atom1d  23697  notnot2ALT  27949
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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