Theorem bj-orim2

Description: Proof of orim2 from the axiomatic definition of disjunction ( olc , orc , jao ) and minimal implicational calculus. (Contributed by BJ, 4-Apr-2021) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-orim2	|- ( ( ph -> ps ) -> ( ( ch \/ ph ) -> ( ch \/ ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		orc	|- ( ch -> ( ch \/ ps ) )
2		olc	|- ( ps -> ( ch \/ ps ) )
3	2	imim2i	|- ( ( ph -> ps ) -> ( ph -> ( ch \/ ps ) ) )
4		jao	|- ( ( ch -> ( ch \/ ps ) ) -> ( ( ph -> ( ch \/ ps ) ) -> ( ( ch \/ ph ) -> ( ch \/ ps ) ) ) )
5	1 3 4	mpsyl	|- ( ( ph -> ps ) -> ( ( ch \/ ph ) -> ( ch \/ ps ) ) )