Theorem frege6

Description: A closed form of imim2d which is a deduction adding nested antecedents. Proposition 6 of Frege1879 p. 33. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege6	|- ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( ( th -> ps ) -> ( th -> ch ) ) ) )

Proof

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