Theorem rp-frege3g

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

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

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

Proof

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