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

Proof

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