Theorem rp-4frege 38096

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

Assertion

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

Proof of Theorem rp-4frege

Step	Hyp	Ref	Expression
1		rp-simp2-frege 38086	. 2 |- ( ( ph -> ( ( ps -> ph ) -> ch ) ) -> ( ph -> ( ps -> ph ) ) )
2		rp-misc1-frege 38090	. 2 |- ( ( ( ph -> ( ( ps -> ph ) -> ch ) ) -> ( ph -> ( ps -> ph ) ) ) -> ( ( ph -> ( ( ps -> ph ) -> ch ) ) -> ( ph -> ch ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -> ( ( ps -> ph ) -> ch ) ) -> ( ph -> ch ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 38084  ax-frege2 38085

This theorem is referenced by:  rp-6frege  38097