Theorem 3exp1

Description: Exportation from left triple conjunction. (Contributed by NM, 24-Feb-2005)

	Ref	Expression
Hypothesis	3exp1.1	$$⊢\left(\left(\phi \wedge \psi \wedge \chi \right)\wedge \theta \right)\to \tau$$
Assertion	3exp1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		3exp1.1	$$⊢\left(\left(\phi \wedge \psi \wedge \chi \right)\wedge \theta \right)\to \tau$$
2	1	ex	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \left(\theta \to \tau \right)$$
3	2	3exp	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$