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Theorem pm2.18da 431
Description: Deduction based on reductio ad absurdum. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
pm2.18da.1  |-  ( (
ph  /\  -.  ps )  ->  ps )
Assertion
Ref Expression
pm2.18da  |-  ( ph  ->  ps )

Proof of Theorem pm2.18da
StepHypRef Expression
1 pm2.18da.1 . . 3  |-  ( (
ph  /\  -.  ps )  ->  ps )
21ex 424 . 2  |-  ( ph  ->  ( -.  ps  ->  ps ) )
32pm2.18d 105 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 359
This theorem is referenced by:  fpwwe2lem13  8509  bpos  21069
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361
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