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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 16 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6
This theorem is referenced by:  mt4i  133  fin1a2s  8035  gchinf  8274  pwfseqlem4  8279  isprm2lem  12759  pcfac  12941  prmreclem3  12959  sylow1lem1  14903  irredrmul  15483  ioorcl2  18921  itg2gt0  19109  mdegmullem  19458  atom1d  22925  notnot2ALT  27563
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
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