Theorem imim1

Description: A closed form of syllogism (see syl ). Theorem *2.06 of WhiteheadRussell p. 100. Its associated inference is imim1i . (Contributed by NM, 29-Dec-1992) (Proof shortened by Wolf Lammen, 25-May-2013)

	Ref	Expression
Assertion	imim1	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜓 → 𝜒 ) → ( 𝜑 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜓 ) )
2	1	imim1d	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜓 → 𝜒 ) → ( 𝜑 → 𝜒 ) ) )