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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  1991  ax10lem4OLD  1996  weniso  6034  ordtypelem10  7452  oismo  7465  rankval3b  7708  grur1  8651  sqeqd  11926  hausflimi  17965  minveclem4  19286  ovolunnul  19349  vitali  19458  itg2mono  19598  pilem3  20322  minvecolem4  22335  frgrancvvdeqlemB  28141  ax10lem4NEW7  29177
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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