Theorem rp-misc1-frege 38090

Description: Double-use of ax-frege2 38085. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
rp-misc1-frege	|- ( ( ( ph -> ( ps -> ch ) ) -> ( ph -> ps ) ) -> ( ( ph -> ( ps -> ch ) ) -> ( ph -> ch ) ) )

Proof of Theorem rp-misc1-frege

Step	Hyp	Ref	Expression
1		ax-frege2 38085	. 2 |- ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )
2		ax-frege2 38085	. 2 |- ( ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) ) -> ( ( ( ph -> ( ps -> ch ) ) -> ( ph -> ps ) ) -> ( ( ph -> ( ps -> ch ) ) -> ( ph -> ch ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ( ph -> ( ps -> ch ) ) -> ( ph -> ps ) ) -> ( ( ph -> ( ps -> ch ) ) -> ( ph -> ch ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  rp-4frege  38096