Theorem frege17 38115

Description: A closed form of com3l 89. Proposition 17 of [Frege1879] p. 39. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege17	|- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ps -> ( ch -> ( ph -> th ) ) ) )

Proof of Theorem frege17

Step	Hyp	Ref	Expression
1		ax-frege8 38103	. 2 |- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ps -> ( ph -> ( ch -> th ) ) ) )
2		frege16 38110	. 2 |- ( ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ps -> ( ph -> ( ch -> th ) ) ) ) -> ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ps -> ( ch -> ( ph -> th ) ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ps -> ( ch -> ( ph -> th ) ) ) )

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:  frege50  38148  frege78  38235