Theorem exp53

Description: An exportation inference. (Contributed by Jeff Hankins, 30-Aug-2009)

	Ref	Expression
Hypothesis	exp53.1	$$⊢\left(\left(\left(\phi \wedge \psi \right)\wedge \left(\chi \wedge \theta \right)\right)\wedge \tau \right)\to \eta$$
Assertion	exp53	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		exp53.1	$$⊢\left(\left(\left(\phi \wedge \psi \right)\wedge \left(\chi \wedge \theta \right)\right)\wedge \tau \right)\to \eta$$
2	1	ex	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \left(\chi \wedge \theta \right)\right)\to \left(\tau \to \eta \right)$$
3	2	exp43	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$