Theorem rp-4frege

Description: Elimination of a nested antecedent of special form. (Contributed by RP, 24-Dec-2019)

	Ref	Expression
Assertion	rp-4frege	$$⊢\left(\phi \to \left(\left(\psi \to \phi \right)\to \chi \right)\right)\to \left(\phi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		rp-simp2-frege	$$⊢\left(\phi \to \left(\left(\psi \to \phi \right)\to \chi \right)\right)\to \left(\phi \to \left(\psi \to \phi \right)\right)$$
2		rp-misc1-frege	$$⊢\left(\left(\phi \to \left(\left(\psi \to \phi \right)\to \chi \right)\right)\to \left(\phi \to \left(\psi \to \phi \right)\right)\right)\to \left(\left(\phi \to \left(\left(\psi \to \phi \right)\to \chi \right)\right)\to \left(\phi \to \chi \right)\right)$$
3	1 2	ax-mp	$$⊢\left(\phi \to \left(\left(\psi \to \phi \right)\to \chi \right)\right)\to \left(\phi \to \chi \right)$$