Theorem frege19 38118

Description: A closed form of syl6 35. Proposition 19 of [Frege1879] p. 39. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege19	|- ( ( ph -> ( ps -> ch ) ) -> ( ( ch -> th ) -> ( ph -> ( ps -> th ) ) ) )

Proof of Theorem frege19

Step	Hyp	Ref	Expression
1		frege9 38106	. 2 |- ( ( ps -> ch ) -> ( ( ch -> th ) -> ( ps -> th ) ) )
2		frege18 38112	. 2 |- ( ( ( ps -> ch ) -> ( ( ch -> th ) -> ( ps -> th ) ) ) -> ( ( ph -> ( ps -> ch ) ) -> ( ( ch -> th ) -> ( ph -> ( ps -> th ) ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -> ( ps -> ch ) ) -> ( ( ch -> th ) -> ( ph -> ( ps -> 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:  frege21  38121  frege20  38122  frege71  38228  frege86  38243  frege103  38260  frege119  38276  frege123  38280