Theorem rp-4frege

Description: Elimination of a nested antecedent of special form. (Contributed by RP, 24-Dec-2019)

	Ref	Expression
Assertion	rp-4frege	|- ( ( ph -> ( ( ps -> ph ) -> ch ) ) -> ( ph -> ch ) )

Proof

Step	Hyp	Ref	Expression
1		rp-simp2-frege	|- ( ( ph -> ( ( ps -> ph ) -> ch ) ) -> ( ph -> ( ps -> ph ) ) )
2		rp-misc1-frege	|- ( ( ( ph -> ( ( ps -> ph ) -> ch ) ) -> ( ph -> ( ps -> ph ) ) ) -> ( ( ph -> ( ( ps -> ph ) -> ch ) ) -> ( ph -> ch ) ) )
3	1 2	ax-mp	|- ( ( ph -> ( ( ps -> ph ) -> ch ) ) -> ( ph -> ch ) )