Theorem wl-luk-pm2.04

Description: Swap antecedents. Theorem *2.04 of WhiteheadRussell p. 100. This was the third axiom in Frege's logic system, specifically Proposition 8 of Frege1879 p. 35. Copy of pm2.04 with a different proof. (Contributed by Wolf Lammen, 7-Jul-2019) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Assertion	wl-luk-pm2.04	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\psi \to \left(\phi \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		wl-luk-ax1	$$⊢\psi \to \left(\phi \to \psi \right)$$
2		wl-luk-ax2	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)$$
3	1 2	wl-luk-imtrid	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\psi \to \left(\phi \to \chi \right)\right)$$