Theorem jaoian

Description: Inference disjoining the antecedents of two implications. (Contributed by NM, 23-Oct-2005)

	Ref	Expression
Hypotheses	jaoian.1	|- ( ( ph /\ ps ) -> ch )
	jaoian.2	|- ( ( th /\ ps ) -> ch )
Assertion	jaoian	|- ( ( ( ph \/ th ) /\ ps ) -> ch )

Proof

Step	Hyp	Ref	Expression
1		jaoian.1	|- ( ( ph /\ ps ) -> ch )
2		jaoian.2	|- ( ( th /\ ps ) -> ch )
3	1	ex	|- ( ph -> ( ps -> ch ) )
4	2	ex	|- ( th -> ( ps -> ch ) )
5	3 4	jaoi	|- ( ( ph \/ th ) -> ( ps -> ch ) )
6	5	imp	|- ( ( ( ph \/ th ) /\ ps ) -> ch )