Theorem exp5k

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

	Ref	Expression
Hypothesis	exp5k.1	$$⊢\phi \to \left(\left(\left(\psi \wedge \left(\chi \wedge \theta \right)\right)\wedge \tau \right)\to \eta \right)$$
Assertion	exp5k	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		exp5k.1	$$⊢\phi \to \left(\left(\left(\psi \wedge \left(\chi \wedge \theta \right)\right)\wedge \tau \right)\to \eta \right)$$
2	1	expd	$$⊢\phi \to \left(\left(\psi \wedge \left(\chi \wedge \theta \right)\right)\to \left(\tau \to \eta \right)\right)$$
3	2	exp4d	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$