Theorem rp-6frege

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

	Ref	Expression
Assertion	rp-6frege	|- ( ph -> ( ( ps -> ( ( ch -> ps ) -> th ) ) -> ( ps -> th ) ) )

Proof

Step	Hyp	Ref	Expression
1		rp-4frege	|- ( ( ps -> ( ( ch -> ps ) -> th ) ) -> ( ps -> th ) )
2		ax-frege1	|- ( ( ( ps -> ( ( ch -> ps ) -> th ) ) -> ( ps -> th ) ) -> ( ph -> ( ( ps -> ( ( ch -> ps ) -> th ) ) -> ( ps -> th ) ) ) )
3	1 2	ax-mp	|- ( ph -> ( ( ps -> ( ( ch -> ps ) -> th ) ) -> ( ps -> th ) ) )