Theorem rp-frege3g 38088

Description: Add antecedent to ax-frege2 38085. More general statement than frege3 38089. Like ax-frege2 38085, it is essentially a closed form of mpd 15, however it has an extra antecedent.

It would be more natural to prove from a1i 11 and ax-frege2 38085 in Metamath. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
rp-frege3g	|- ( ph -> ( ( ps -> ( ch -> th ) ) -> ( ( ps -> ch ) -> ( ps -> th ) ) ) )

Proof of Theorem rp-frege3g

Step	Hyp	Ref	Expression
1		ax-frege2 38085	. 2 |- ( ( ps -> ( ch -> th ) ) -> ( ( ps -> ch ) -> ( ps -> th ) ) )
2		ax-frege1 38084	. 2 |- ( ( ( ps -> ( ch -> th ) ) -> ( ( ps -> ch ) -> ( ps -> th ) ) ) -> ( ph -> ( ( ps -> ( ch -> th ) ) -> ( ( ps -> ch ) -> ( ps -> th ) ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ph -> ( ( ps -> ( ch -> th ) ) -> ( ( ps -> ch ) -> ( ps -> th ) ) ) )

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-frege4g  38092