Theorem jaao

Description: Inference conjoining and disjoining the antecedents of two implications. (Contributed by NM, 30-Sep-1999)

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

Proof

Step	Hyp	Ref	Expression
1		jaao.1	|- ( ph -> ( ps -> ch ) )
2		jaao.2	|- ( th -> ( ta -> ch ) )
3	1	adantr	|- ( ( ph /\ th ) -> ( ps -> ch ) )
4	2	adantl	|- ( ( ph /\ th ) -> ( ta -> ch ) )
5	3 4	jaod	|- ( ( ph /\ th ) -> ( ( ps \/ ta ) -> ch ) )