Theorem frege21 38121

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

Assertion

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

Proof of Theorem frege21

Step	Hyp	Ref	Expression
1		frege9 38106	. 2 |- ( ( ph -> th ) -> ( ( th -> ps ) -> ( ph -> ps ) ) )
2		frege19 38118	. 2 |- ( ( ( ph -> th ) -> ( ( th -> ps ) -> ( ph -> ps ) ) ) -> ( ( ( ph -> ps ) -> ch ) -> ( ( ph -> th ) -> ( ( th -> ps ) -> ch ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ( ph -> ps ) -> ch ) -> ( ( ph -> th ) -> ( ( th -> ps ) -> ch ) ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 38084  ax-frege2 38085  ax-frege8 38103

This theorem is referenced by:  frege44  38142  frege47  38145