Theorem jaoa

Description: Inference disjoining and conjoining the antecedents of two implications. (Contributed by Stefan Allan, 1-Nov-2008)

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

Proof

Step	Hyp	Ref	Expression
1		jaao.1	|- ( ph -> ( ps -> ch ) )
2		jaao.2	|- ( th -> ( ta -> ch ) )
3	1	adantrd	|- ( ph -> ( ( ps /\ ta ) -> ch ) )
4	2	adantld	|- ( th -> ( ( ps /\ ta ) -> ch ) )
5	3 4	jaoi	|- ( ( ph \/ th ) -> ( ( ps /\ ta ) -> ch ) )