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Theorem 3ornot23 31526
Description: If the second and third disjuncts of a true triple disjunction are false, then the first disjunct is true. Automatically derived from 3ornot23VD 31896. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
3ornot23  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ( ch  \/  ph  \/  ps )  ->  ch ) )

Proof of Theorem 3ornot23
StepHypRef Expression
1 idd 24 . . 3  |-  ( -. 
ph  ->  ( ch  ->  ch ) )
2 pm2.21 108 . . 3  |-  ( -. 
ph  ->  ( ph  ->  ch ) )
3 pm2.21 108 . . 3  |-  ( -. 
ps  ->  ( ps  ->  ch ) )
41, 2, 33jaao 1287 . 2  |-  ( ( -.  ph  /\  -.  ph  /\ 
-.  ps )  ->  (
( ch  \/  ph  \/  ps )  ->  ch ) )
543anidm12 1276 1  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ( ch  \/  ph  \/  ps )  ->  ch ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 369    \/ w3o 964
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-or 370  df-an 371  df-3or 966  df-3an 967
This theorem is referenced by:  tratrb  31555  tratrbVD  31910
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