Theorem axfrege8

Description: Swap antecedents. Identical to pm2.04 . This demonstrates that Axiom 8 of Frege1879 p. 35 is redundant.

Proof follows closely proof of pm2.04 in https://us.metamath.org/mmsolitaire/pmproofs.txt , but in the style of Frege's 1879 work. (Contributed by RP, 24-Dec-2019) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Assertion	axfrege8	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\psi \to \left(\phi \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		rp-7frege	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\psi \to \left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)\right)$$
2		rp-8frege	$$⊢\left(\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\psi \to \left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)\right)\right)\to \left(\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\psi \to \left(\phi \to \chi \right)\right)\right)$$
3	1 2	ax-mp	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\psi \to \left(\phi \to \chi \right)\right)$$