Theorem frege6 38100

Description: A closed form of imim2d 57 which is a deduction adding nested antecedents. Proposition 6 of [Frege1879] p. 33. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

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

Proof of Theorem frege6

Step	Hyp	Ref	Expression
1		frege5 38094	. 2 |- ( ( ps -> ch ) -> ( ( th -> ps ) -> ( th -> ch ) ) )
2		frege5 38094	. 2 |- ( ( ( ps -> ch ) -> ( ( th -> ps ) -> ( th -> ch ) ) ) -> ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( ( th -> ps ) -> ( th -> ch ) ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( ( th -> ps ) -> ( th -> ch ) ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  frege7  38102