Theorem expt

Description: Exportation theorem pm3.3 (closed form of ex ) expressed with primitive connectives. (Contributed by NM, 28-Dec-1992)

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

Proof

Step	Hyp	Ref	Expression
1		pm3.2im	$$⊢\phi \to \left(\psi \to \neg \left(\phi \to \neg \psi \right)\right)$$
2	1	imim1d	$$⊢\phi \to \left(\left(\neg \left(\phi \to \neg \psi \right)\to \chi \right)\to \left(\psi \to \chi \right)\right)$$
3	2	com12	$$⊢\left(\neg \left(\phi \to \neg \psi \right)\to \chi \right)\to \left(\phi \to \left(\psi \to \chi \right)\right)$$