Theorem 3ornot23 33665

Description: If the second and third disjuncts of a true triple disjunction are false, then the first disjunct is true. Automatically derived from 3ornot23VD 34047. (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

Step	Hyp	Ref	Expression
1		idd 24	. . 3 |- ( -. ph -> ( ch -> ch ) )
2		pm2.21 108	. . 3 |- ( -. ph -> ( ph -> ch ) )
3		pm2.21 108	. . 3 |- ( -. ps -> ( ps -> ch ) )
4	1, 2, 3	3jaao 1294	. 2 |- ( ( -. ph /\ -. ph /\ -. ps ) -> ( ( ch \/ ph \/ ps ) -> ch ) )
5	4	3anidm12 1283	1 |- ( ( -. ph /\ -. ps ) -> ( ( ch \/ ph \/ ps ) -> ch ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 367   \/ w3o 970

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 368  df-an 369  df-3or 972  df-3an 973

This theorem is referenced by:  tratrb  33697  tratrbVD  34062