Theorem adh-minimp-ax2-lem4

Description: Fourth lemma for the derivation of ax-2 from adh-minimp and ax-mp . Polish prefix notation: CpCCqCprCqr . (Contributed by ADH, 10-Nov-2023) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	adh-minimp-ax2-lem4	|- ( ph -> ( ( ps -> ( ph -> ch ) ) -> ( ps -> ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		adh-minimp-ax2c	|- ( ( ps -> ph ) -> ( ( ps -> ( ph -> ch ) ) -> ( ps -> ch ) ) )
2		adh-minimp-sylsimp	|- ( ( ( ps -> ph ) -> ( ( ps -> ( ph -> ch ) ) -> ( ps -> ch ) ) ) -> ( ph -> ( ( ps -> ( ph -> ch ) ) -> ( ps -> ch ) ) ) )
3	1 2	ax-mp	|- ( ph -> ( ( ps -> ( ph -> ch ) ) -> ( ps -> ch ) ) )