Theorem wl-luk-imim2

Description: A closed form of syllogism (see syl ). Theorem *2.05 of WhiteheadRussell p. 100. Copy of imim2 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Assertion	wl-luk-imim2	$$⊢\left(\phi \to \psi \right)\to \left(\left(\chi \to \phi \right)\to \left(\chi \to \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ax-luk1	$$⊢\left(\chi \to \phi \right)\to \left(\left(\phi \to \psi \right)\to \left(\chi \to \psi \right)\right)$$
2	1	wl-luk-com12	$$⊢\left(\phi \to \psi \right)\to \left(\left(\chi \to \phi \right)\to \left(\chi \to \psi \right)\right)$$