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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  5704  ordtypelem10  7126  oismo  7139  rankval3b  7382  fpwwe2lem13  8144  grur1  8322  sqeqd  11528  hausflimi  17507  minveclem4  18628  ovolunnul  18691  vitali  18800  itg2mono  18940  pilem3  19661  bpos  20364  minvecolem4  21289  isunscov  24239  bwt2  24758
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
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