Theorem rp-frege24 38091

Description: Introducing an embedded antecedent. Alternate proof for frege24 38109. Closed form for a1d 25. (Contributed by RP, 24-Dec-2019.)

Assertion

Ref	Expression
rp-frege24	|- ( ( ph -> ps ) -> ( ph -> ( ch -> ps ) ) )

Proof of Theorem rp-frege24

Step	Hyp	Ref	Expression
1		rp-simp2-frege 38086	. 2 |- ( ph -> ( ps -> ( ch -> ps ) ) )
2		ax-frege2 38085	. 2 |- ( ( ph -> ( ps -> ( ch -> ps ) ) ) -> ( ( ph -> ps ) -> ( ph -> ( ch -> ps ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -> ps ) -> ( ph -> ( ch -> ps ) ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 38084  ax-frege2 38085

This theorem is referenced by:  rp-7frege  38095  rp-frege25  38099