Theorem imim2

Description: A closed form of syllogism (see syl ). Theorem *2.05 of WhiteheadRussell p. 100. Its associated inference is imim2i . Its associated deduction is imim2d . An alternate proof from more basic results is given by ax-1 followed by a2d . (Contributed by NM, 29-Dec-1992) (Proof shortened by Wolf Lammen, 6-Sep-2012)

	Ref	Expression
Assertion	imim2	$$⊢\left(\phi \to \psi \right)\to \left(\left(\chi \to \phi \right)\to \left(\chi \to \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \psi \right)$$
2	1	imim2d	$$⊢\left(\phi \to \psi \right)\to \left(\left(\chi \to \phi \right)\to \left(\chi \to \psi \right)\right)$$