Theorem frege16 38110

Description: A closed form of com34 91. Proposition 16 of [Frege1879] p. 38. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege16	|- ( ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) ) -> ( ph -> ( ps -> ( th -> ( ch -> ta ) ) ) ) )

Proof of Theorem frege16

Step	Hyp	Ref	Expression
1		frege12 38107	. 2 |- ( ( ps -> ( ch -> ( th -> ta ) ) ) -> ( ps -> ( th -> ( ch -> ta ) ) ) )
2		frege5 38094	. 2 |- ( ( ( ps -> ( ch -> ( th -> ta ) ) ) -> ( ps -> ( th -> ( ch -> ta ) ) ) ) -> ( ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) ) -> ( ph -> ( ps -> ( th -> ( ch -> ta ) ) ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) ) -> ( ph -> ( ps -> ( th -> ( ch -> ta ) ) ) ) )

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:  frege18  38112  frege22  38113  frege17  38115