Theorem axfrege8 38101

Description: Swap antecedents. Identical to pm2.04 90. This demonstrates that Axiom 8 of [Frege1879] p. 35 is redundant.

Proof follows closely proof of pm2.04 90 in http://us.metamath.org/mmsolitaire/pmproofs.txt, but in the style of Frege's 1879 work. (Contributed by RP, 24-Dec-2019.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
axfrege8	|- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ph -> ch ) ) )

Proof of Theorem axfrege8

Step	Hyp	Ref	Expression
1		rp-7frege 38095	. 2 |- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ( ph -> ps ) -> ( ph -> ch ) ) ) )
2		rp-8frege 38098	. 2 |- ( ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ( ph -> ps ) -> ( ph -> ch ) ) ) ) -> ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ph -> ch ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ph -> 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: (None)