Axiom ax-frege8

Description: Swap antecedents. If two conditions have a proposition as a consequence, their order is immaterial. Third axiom of Frege's 1879 work but identical to pm2.04 which can be proved from only ax-mp , ax-frege1 , and ax-frege2 . (Redundant) Axiom 8 of Frege1879 p. 35. (Contributed by RP, 24-Dec-2019) (New usage is discouraged.)

	Ref	Expression
Assertion	ax-frege8	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\psi \to \left(\phi \to \chi \right)\right)$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		wph	$$wff\phi$$
1		wps	$$wff\psi$$
2		wch	$$wff\chi$$
3	1 2	wi	$$wff\left(\psi \to \chi \right)$$
4	0 3	wi	$$wff\left(\phi \to \left(\psi \to \chi \right)\right)$$
5	0 2	wi	$$wff\left(\phi \to \chi \right)$$
6	1 5	wi	$$wff\left(\psi \to \left(\phi \to \chi \right)\right)$$
7	4 6	wi	$$wff\left(\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\psi \to \left(\phi \to \chi \right)\right)\right)$$