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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  7973  gchinf  8212  pwfseqlem4  8217  isprm2lem  12692  pcfac  12874  prmreclem3  12892  sylow1lem1  14836  irredrmul  15416  ioorcl2  18854  itg2gt0  19042  mdegmullem  19391  atom1d  22858  notnot2ALT  27308
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
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