Theorem frege24 38109

Description: Closed form for a1d 25. Deduction introducing an embedded antecedent. Identical to rp-frege24 38091 which was proved without relying on ax-frege8 38103. Proposition 24 of [Frege1879] p. 42. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

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

Proof of Theorem frege24

Step	Hyp	Ref	Expression
1		ax-frege1 38084	. 2 |- ( ( ph -> ps ) -> ( ch -> ( ph -> ps ) ) )
2		frege12 38107	. 2 |- ( ( ( ph -> ps ) -> ( ch -> ( ph -> 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  ax-frege8 38103

This theorem is referenced by:  frege25  38111  frege63a  38175  frege63b  38202  frege63c  38220