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	⊢ ( 𝜑 → 𝜓 )
	wl-luk-syl.2	⊢ ( 𝜓 → 𝜒 )
Assertion	wl-luk-syl	⊢ ( 𝜑 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		wl-luk-syl.1	⊢ ( 𝜑 → 𝜓 )
2		wl-luk-syl.2	⊢ ( 𝜓 → 𝜒 )
3	1	wl-luk-imim1i	⊢ ( ( 𝜓 → 𝜒 ) → ( 𝜑 → 𝜒 ) )
4	2 3	ax-mp	⊢ ( 𝜑 → 𝜒 )