Theorem rp-simp2-frege

Description: Simplification of triple conjunction. Compare with simp2 . (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	rp-simp2-frege	$$⊢\phi \to \left(\psi \to \left(\chi \to \psi \right)\right)$$

Proof

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