Theorem frege10 38114

Description: Result commuting antecedents within an antecedent. Proposition 10 of [Frege1879] p. 36. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege10	|- ( ( ( ph -> ( ps -> ch ) ) -> th ) -> ( ( ps -> ( ph -> ch ) ) -> th ) )

Proof of Theorem frege10

Step	Hyp	Ref	Expression
1		ax-frege8 38103	. 2 |- ( ( ps -> ( ph -> ch ) ) -> ( ph -> ( ps -> ch ) ) )
2		frege9 38106	. 2 |- ( ( ( ps -> ( ph -> ch ) ) -> ( ph -> ( ps -> ch ) ) ) -> ( ( ( ph -> ( ps -> ch ) ) -> th ) -> ( ( ps -> ( ph -> ch ) ) -> th ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ( ph -> ( ps -> ch ) ) -> th ) -> ( ( ps -> ( ph -> ch ) ) -> 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:  frege30  38126