Theorem orim12i

Description: Disjoin antecedents and consequents of two premises. (Contributed by NM, 6-Jun-1994) (Proof shortened by Wolf Lammen, 25-Jul-2012)

	Ref	Expression
Hypotheses	orim12i.1	|- ( ph -> ps )
	orim12i.2	|- ( ch -> th )
Assertion	orim12i	|- ( ( ph \/ ch ) -> ( ps \/ th ) )

Proof

Step	Hyp	Ref	Expression
1		orim12i.1	|- ( ph -> ps )
2		orim12i.2	|- ( ch -> th )
3	1	orcd	|- ( ph -> ( ps \/ th ) )
4	2	olcd	|- ( ch -> ( ps \/ th ) )
5	3 4	jaoi	|- ( ( ph \/ ch ) -> ( ps \/ th ) )