Theorem jaod

Description: Deduction disjoining the antecedents of two implications. (Contributed by NM, 18-Aug-1994)

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

Proof

Step	Hyp	Ref	Expression
1		jaod.1	|- ( ph -> ( ps -> ch ) )
2		jaod.2	|- ( ph -> ( th -> ch ) )
3	1	com12	|- ( ps -> ( ph -> ch ) )
4	2	com12	|- ( th -> ( ph -> ch ) )
5	3 4	jaoi	|- ( ( ps \/ th ) -> ( ph -> ch ) )
6	5	com12	|- ( ph -> ( ( ps \/ th ) -> ch ) )