Theorem 3ori

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

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

Proof

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