Theorem rp-frege24

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

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

Proof

Step	Hyp	Ref	Expression
1		rp-simp2-frege	$$⊢\phi \to \left(\psi \to \left(\chi \to \psi \right)\right)$$
2		ax-frege2	$$⊢\left(\phi \to \left(\psi \to \left(\chi \to \psi \right)\right)\right)\to \left(\left(\phi \to \psi \right)\to \left(\phi \to \left(\chi \to \psi \right)\right)\right)$$
3	1 2	ax-mp	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \left(\chi \to \psi \right)\right)$$