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Theorem pm2.01da 442
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 434 . 2  |-  ( ph  ->  ( ps  ->  -.  ps ) )
32pm2.01d 169 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  efrirr  4701  omlimcl  7017  hartogslem1  7756  cfslb2n  8437  fin23lem41  8521  tskuni  8950  4sqlem18  14023  ramlb  14080  ivthlem2  20936  ivthlem3  20937  cosne0  21986
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