Theorem 3expd

Description: Exportation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006)

	Ref	Expression
Hypothesis	3expd.1	$$⊢\phi \to \left(\left(\psi \wedge \chi \wedge \theta \right)\to \tau \right)$$
Assertion	3expd	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		3expd.1	$$⊢\phi \to \left(\left(\psi \wedge \chi \wedge \theta \right)\to \tau \right)$$
2	1	com12	$$⊢\left(\psi \wedge \chi \wedge \theta \right)\to \left(\phi \to \tau \right)$$
3	2	3exp	$$⊢\psi \to \left(\chi \to \left(\theta \to \left(\phi \to \tau \right)\right)\right)$$
4	3	com4r	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$