Theorem jaoded

Description: Deduction form of jao . Disjunction of antecedents. (Contributed by Alan Sare, 3-Dec-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	jaoded.1	|- ( ph -> ( ps -> ch ) )
	jaoded.2	|- ( th -> ( ta -> ch ) )
	jaoded.3	|- ( et -> ( ps \/ ta ) )
Assertion	jaoded	|- ( ( ph /\ th /\ et ) -> ch )

Proof

Step	Hyp	Ref	Expression
1		jaoded.1	|- ( ph -> ( ps -> ch ) )
2		jaoded.2	|- ( th -> ( ta -> ch ) )
3		jaoded.3	|- ( et -> ( ps \/ ta ) )
4		jao	|- ( ( ps -> ch ) -> ( ( ta -> ch ) -> ( ( ps \/ ta ) -> ch ) ) )
5	4	3imp	|- ( ( ( ps -> ch ) /\ ( ta -> ch ) /\ ( ps \/ ta ) ) -> ch )
6	1 2 3 5	syl3an	|- ( ( ph /\ th /\ et ) -> ch )