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Theorem pm2.18d 105
Description: Deduction based on reductio ad absurdum. (Contributed by FL, 12-Jul-2009.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Hypothesis
Ref Expression
pm2.18d.1  |-  ( ph  ->  ( -.  ps  ->  ps ) )
Assertion
Ref Expression
pm2.18d  |-  ( ph  ->  ps )

Proof of Theorem pm2.18d
StepHypRef Expression
1 pm2.18d.1 . 2  |-  ( ph  ->  ( -.  ps  ->  ps ) )
2 pm2.18 104 . 2  |-  ( ( -.  ps  ->  ps )  ->  ps )
31, 2syl 16 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  notnot2  106  pm2.61d  152  pm2.18da  431  oplem1  931  ax10  1984  ax10lem4OLD  1988  weniso  6015  ordtypelem10  7430  oismo  7443  rankval3b  7686  grur1  8629  sqeqd  11899  hausflimi  17934  minveclem4  19201  ovolunnul  19264  vitali  19373  itg2mono  19513  pilem3  20237  minvecolem4  22231  frgrancvvdeqlemB  27791  ax10lem4NEW7  28810
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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