Theorem exp512

Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009)

	Ref	Expression
Hypothesis	exp512.1	$$⊢\left(\phi \wedge \left(\left(\psi \wedge \chi \right)\wedge \left(\theta \wedge \tau \right)\right)\right)\to \eta$$
Assertion	exp512	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		exp512.1	$$⊢\left(\phi \wedge \left(\left(\psi \wedge \chi \right)\wedge \left(\theta \wedge \tau \right)\right)\right)\to \eta$$
2	1	ex	$$⊢\phi \to \left(\left(\left(\psi \wedge \chi \right)\wedge \left(\theta \wedge \tau \right)\right)\to \eta \right)$$
3	2	exp5l	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$