Theorem 3imp1

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

	Ref	Expression
Hypothesis	3imp1.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$
Assertion	3imp1	$$⊢\left(\left(\phi \wedge \psi \wedge \chi \right)\wedge \theta \right)\to \tau$$

Proof

Step	Hyp	Ref	Expression
1		3imp1.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$
2	1	3imp	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \left(\theta \to \tau \right)$$
3	2	imp	$$⊢\left(\left(\phi \wedge \psi \wedge \chi \right)\wedge \theta \right)\to \tau$$