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Theorem efald 1343
Description: Deduction based on reductio ad absurdum. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
efald.1  |-  ( (
ph  /\  -.  ps )  ->  F.  )
Assertion
Ref Expression
efald  |-  ( ph  ->  ps )

Proof of Theorem efald
StepHypRef Expression
1 efald.1 . . 3  |-  ( (
ph  /\  -.  ps )  ->  F.  )
21inegd 1342 . 2  |-  ( ph  ->  -.  -.  ps )
32notnotrd 107 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 359    F. wfal 1326
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  df-tru 1328  df-fal 1329
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