Theorem 3ori 1242

Description: Infer implication from triple disjunction. (Contributed by NM, 26-Sep-2006.)

Hypothesis

Ref	Expression
3ori.1	|- (ph \/ ps \/ ch)

Assertion

Ref	Expression
3ori	|- ((-. ph /\ -. ps) -> ch)

Proof of Theorem 3ori

Step	Hyp	Ref	Expression
1		ioran 476	. 2 |- (-. (ph \/ ps) <-> (-. ph /\ -. ps))
2		3ori.1	. . . 4 |- (ph \/ ps \/ ch)
3		df-3or 935	. . . 4 |- ((ph \/ ps \/ ch) <-> ((ph \/ ps) \/ ch))
4	2, 3	mpbi 199	. . 3 |- ((ph \/ ps) \/ ch)
5	4	ori 364	. 2 |- (-. (ph \/ ps) -> ch)
6	1, 5	sylbir 204	1 |- ((-. ph /\ -. ps) -> ch)

Syntax hints:  -. wn 3   -> wi 4   \/ wo 357   /\ wa 358   \/ w3o 933

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 177  df-or 359  df-an 360  df-3or 935

This theorem is referenced by: (None)