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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 17 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6
This theorem is referenced by:  notnot2  106  pm2.61d  152  pm2.18da  432  oplem1  935  ax10lem26  1675  weniso  5786  ordtypelem10  7210  oismo  7223  rankval3b  7466  fpwwe2lem13  8232  grur1  8410  sqeqd  11617  hausflimi  17638  minveclem4  18759  ovolunnul  18822  vitali  18931  itg2mono  19071  pilem3  19792  bpos  20495  minvecolem4  21420  isunscov  24441  bwt2  24960  ax10lem26X  28345
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
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