Theorem wl-luk-imtrid

Description: A syllogism rule of inference. The first premise is used to replace the second antecedent of the second premise. Copy of syl5 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018) (New usage is discouraged.) (Proof modification is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		wl-luk-imtrid.1	$$⊢\phi \to \psi$$
2		wl-luk-imtrid.2	$$⊢\chi \to \left(\psi \to \theta \right)$$
3	1	wl-luk-imim1i	$$⊢\left(\psi \to \theta \right)\to \left(\phi \to \theta \right)$$
4	2 3	wl-luk-syl	$$⊢\chi \to \left(\phi \to \theta \right)$$