Theorem wl-luk-imim2

Description: A closed form of syllogism (see syl ). Theorem *2.05 of WhiteheadRussell p. 100. Copy of imim2 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Assertion	wl-luk-imim2	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → 𝜑 ) → ( 𝜒 → 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ax-luk1	⊢ ( ( 𝜒 → 𝜑 ) → ( ( 𝜑 → 𝜓 ) → ( 𝜒 → 𝜓 ) ) )
2	1	wl-luk-com12	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → 𝜑 ) → ( 𝜒 → 𝜓 ) ) )