Theorem frege24

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

	Ref	Expression
Assertion	frege24	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \left(\chi \to \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ax-frege1	$$⊢\left(\phi \to \psi \right)\to \left(\chi \to \left(\phi \to \psi \right)\right)$$
2		frege12	$$⊢\left(\left(\phi \to \psi \right)\to \left(\chi \to \left(\phi \to \psi \right)\right)\right)\to \left(\left(\phi \to \psi \right)\to \left(\phi \to \left(\chi \to \psi \right)\right)\right)$$
3	1 2	ax-mp	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \left(\chi \to \psi \right)\right)$$