Theorem jaoi

Description: Inference disjoining the antecedents of two implications. (Contributed by NM, 5-Apr-1994)

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

Proof

Step	Hyp	Ref	Expression
1		jaoi.1	|- ( ph -> ps )
2		jaoi.2	|- ( ch -> ps )
3		pm2.53	|- ( ( ph \/ ch ) -> ( -. ph -> ch ) )
4	3 2	syl6	|- ( ( ph \/ ch ) -> ( -. ph -> ps ) )
5	4 1	pm2.61d2	|- ( ( ph \/ ch ) -> ps )