Theorem wl-luk-syl

Description: An inference version of the transitive laws for implication luk-1 . Copy of syl with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	wl-luk-syl.1	$$⊢\phi \to \psi$$
	wl-luk-syl.2	$$⊢\psi \to \chi$$
Assertion	wl-luk-syl	$$⊢\phi \to \chi$$

Proof

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