Theorem 3expib

Description: Exportation from triple conjunction. (Contributed by NM, 19-May-2007)

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

Proof

Step	Hyp	Ref	Expression
1		3exp.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
2	1	3exp	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
3	2	impd	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$