Theorem exp516

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

	Ref	Expression
Hypothesis	exp516.1	$$⊢\left(\left(\phi \wedge \left(\psi \wedge \chi \wedge \theta \right)\right)\wedge \tau \right)\to \eta$$
Assertion	exp516	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		exp516.1	$$⊢\left(\left(\phi \wedge \left(\psi \wedge \chi \wedge \theta \right)\right)\wedge \tau \right)\to \eta$$
2	1	exp31	$$⊢\phi \to \left(\left(\psi \wedge \chi \wedge \theta \right)\to \left(\tau \to \eta \right)\right)$$
3	2	3expd	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$