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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  7924  gchinf  8159  pwfseqlem4  8164  isprm2lem  12639  pcfac  12821  prmreclem3  12839  sylow1lem1  14744  irredrmul  15324  ioorcl2  18759  itg2gt0  18947  mdegmullem  19296  atom1d  22763  notnot2ALT  26985
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
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