Theorem frege12

Description: A closed form of com23 . Proposition 12 of Frege1879 p. 37. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege12	|- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ph -> ( ch -> ( ps -> th ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		ax-frege8	|- ( ( ps -> ( ch -> th ) ) -> ( ch -> ( ps -> th ) ) )
2		frege5	|- ( ( ( ps -> ( ch -> th ) ) -> ( ch -> ( ps -> th ) ) ) -> ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ph -> ( ch -> ( ps -> th ) ) ) ) )
3	1 2	ax-mp	|- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ph -> ( ch -> ( ps -> th ) ) ) )