Theorem exp5d

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

	Ref	Expression
Hypothesis	exp5d.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \left(\left(\theta \wedge \tau \right)\to \eta \right)$$
Assertion	exp5d	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		exp5d.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \left(\left(\theta \wedge \tau \right)\to \eta \right)$$
2	1	expd	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \left(\theta \to \left(\tau \to \eta \right)\right)$$
3	2	exp31	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$