Theorem jaodan

Description: Deduction disjoining the antecedents of two implications. (Contributed by NM, 14-Oct-2005)

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

Proof

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