Theorem bj-orim2 32541

Description: Proof of orim2 886 from the axiomatic definition of disjunction (olc 399, orc 400, jao 534) and minimal implicational calculus. (Contributed by BJ, 4-Apr-2021.) (Proof modification is discouraged.)

Assertion

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

Proof of Theorem bj-orim2

Step	Hyp	Ref	Expression
1		orc 400	. 2 |- ( ch -> ( ch \/ ps ) )
2		olc 399	. . 3 |- ( ps -> ( ch \/ ps ) )
3	2	imim2i 16	. 2 |- ( ( ph -> ps ) -> ( ph -> ( ch \/ ps ) ) )
4		jao 534	. 2 |- ( ( ch -> ( ch \/ ps ) ) -> ( ( ph -> ( ch \/ ps ) ) -> ( ( ch \/ ph ) -> ( ch \/ ps ) ) ) )
5	1, 3, 4	mpsyl 68	1 |- ( ( ph -> ps ) -> ( ( ch \/ ph ) -> ( ch \/ ps ) ) )

Syntax hints:   -> wi 4   \/ wo 383

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386

This theorem is referenced by:  bj-peirce  32543