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Theorem pm2.01da 430
Description: Deduction based on reductio ad absurdum. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
pm2.01da.1  |-  ( (
ph  /\  ps )  ->  -.  ps )
Assertion
Ref Expression
pm2.01da  |-  ( ph  ->  -.  ps )

Proof of Theorem pm2.01da
StepHypRef Expression
1 pm2.01da.1 . . 3  |-  ( (
ph  /\  ps )  ->  -.  ps )
21ex 424 . 2  |-  ( ph  ->  ( ps  ->  -.  ps ) )
32pm2.01d 163 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 359
This theorem is referenced by:  efrirr  4555  omlimcl  6813  hartogslem1  7503  cfslb2n  8140  fin23lem41  8224  tskuni  8650  4sqlem18  13322  ramlb  13379  ivthlem2  19341  ivthlem3  19342  cosne0  20424
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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