Theorem 3exp2

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

	Ref	Expression
Hypothesis	3exp2.1	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \wedge \theta \right)\right)\to \tau$$
Assertion	3exp2	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		3exp2.1	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \wedge \theta \right)\right)\to \tau$$
2	1	ex	$$⊢\phi \to \left(\left(\psi \wedge \chi \wedge \theta \right)\to \tau \right)$$
3	2	3expd	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$