Theorem exp45

Description: An exportation inference. (Contributed by NM, 26-Apr-1994)

	Ref	Expression
Hypothesis	exp45.1	$$⊢\left(\phi \wedge \left(\psi \wedge \left(\chi \wedge \theta \right)\right)\right)\to \tau$$
Assertion	exp45	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		exp45.1	$$⊢\left(\phi \wedge \left(\psi \wedge \left(\chi \wedge \theta \right)\right)\right)\to \tau$$
2	1	exp32	$$⊢\phi \to \left(\psi \to \left(\left(\chi \wedge \theta \right)\to \tau \right)\right)$$
3	2	exp4a	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$