Theorem exp5o

Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009)

	Ref	Expression
Hypothesis	exp5o.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \left(\left(\theta \wedge \tau \right)\to \eta \right)$$
Assertion	exp5o	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		exp5o.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \left(\left(\theta \wedge \tau \right)\to \eta \right)$$
2	1	expd	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \left(\theta \to \left(\tau \to \eta \right)\right)$$
3	2	3exp	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$