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Theorem condan 769
Description: Proof by contradiction. (Contributed by NM, 9-Feb-2006.) (Proof shortened by Wolf Lammen, 19-Jun-2014.)
Hypotheses
Ref Expression
condan.1  |-  ( (
ph  /\  -.  ps )  ->  ch )
condan.2  |-  ( (
ph  /\  -.  ps )  ->  -.  ch )
Assertion
Ref Expression
condan  |-  ( ph  ->  ps )

Proof of Theorem condan
StepHypRef Expression
1 condan.1 . . 3  |-  ( (
ph  /\  -.  ps )  ->  ch )
2 condan.2 . . 3  |-  ( (
ph  /\  -.  ps )  ->  -.  ch )
31, 2pm2.65da 559 . 2  |-  ( ph  ->  -.  -.  ps )
4 notnot2 104 . 2  |-  ( -. 
-.  ps  ->  ps )
53, 4syl 15 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 358
This theorem is referenced by:  rlimcld2  12052  perfectlem2  20469  ballotlemfc0  23051  ballotlemi1  23061  ballotlemii  23062  ballotlemic  23065  stoweidlem52  27801
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 177  df-an 360
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