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	$$⊢\left(\phi \to \psi \right)\to \left(\left(\psi \to \chi \right)\to \left(\phi \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \psi \right)$$
2	1	imim1d	$$⊢\left(\phi \to \psi \right)\to \left(\left(\psi \to \chi \right)\to \left(\phi \to \chi \right)\right)$$