Theorem frege21

Description: Replace antecedent in antecedent. Proposition 21 of Frege1879 p. 40. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege21	|- ( ( ( ph -> ps ) -> ch ) -> ( ( ph -> th ) -> ( ( th -> ps ) -> ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		frege9	|- ( ( ph -> th ) -> ( ( th -> ps ) -> ( ph -> ps ) ) )
2		frege19	|- ( ( ( ph -> th ) -> ( ( th -> ps ) -> ( ph -> ps ) ) ) -> ( ( ( ph -> ps ) -> ch ) -> ( ( ph -> th ) -> ( ( th -> ps ) -> ch ) ) ) )
3	1 2	ax-mp	|- ( ( ( ph -> ps ) -> ch ) -> ( ( ph -> th ) -> ( ( th -> ps ) -> ch ) ) )