Theorem wl-luk-imtrdi

Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. Copy of syl6 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	wl-luk-imtrdi.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	wl-luk-imtrdi.2	$$⊢\chi \to \theta$$
Assertion	wl-luk-imtrdi	$$⊢\phi \to \left(\psi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		wl-luk-imtrdi.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		wl-luk-imtrdi.2	$$⊢\chi \to \theta$$
3	2	wl-luk-imim2i	$$⊢\left(\psi \to \chi \right)\to \left(\psi \to \theta \right)$$
4	1 3	wl-luk-syl	$$⊢\phi \to \left(\psi \to \theta \right)$$