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Theorem condis 24942
Description: Proof by contradiction combined with a disjunction. (Contributed by FL, 20-Apr-2011.)
Hypotheses
Ref Expression
condis.1  |-  ( ph  ->  ps )
condis.2  |-  ( -. 
ph  ->  ch )
Assertion
Ref Expression
condis  |-  ( ps  \/  ch )

Proof of Theorem condis
StepHypRef Expression
1 exmid 404 . 2  |-  ( ph  \/  -.  ph )
2 condis.1 . . 3  |-  ( ph  ->  ps )
3 condis.2 . . 3  |-  ( -. 
ph  ->  ch )
42, 3orim12i 502 . 2  |-  ( (
ph  \/  -.  ph )  ->  ( ps  \/  ch ) )
51, 4ax-mp 8 1  |-  ( ps  \/  ch )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 357
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-or 359
  Copyright terms: Public domain W3C validator