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

Proof

Step	Hyp	Ref	Expression
1		wl-luk-imtrdi.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		wl-luk-imtrdi.2	⊢ ( 𝜒 → 𝜃 )
3	2	wl-luk-imim2i	⊢ ( ( 𝜓 → 𝜒 ) → ( 𝜓 → 𝜃 ) )
4	1 3	wl-luk-syl	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )