Theorem pm2.83

Description: Theorem *2.83 of WhiteheadRussell p. 108. Closed form of syld . (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm2.83	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\left(\phi \to \left(\chi \to \theta \right)\right)\to \left(\phi \to \left(\psi \to \theta \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		imim1	$$⊢\left(\psi \to \chi \right)\to \left(\left(\chi \to \theta \right)\to \left(\psi \to \theta \right)\right)$$
2	1	imim3i	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\left(\phi \to \left(\chi \to \theta \right)\right)\to \left(\phi \to \left(\psi \to \theta \right)\right)\right)$$