Theorem imp55

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

	Ref	Expression
Hypothesis	imp5.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$
Assertion	imp55	$$⊢\left(\left(\phi \wedge \left(\psi \wedge \left(\chi \wedge \theta \right)\right)\right)\wedge \tau \right)\to \eta$$

Proof

Step	Hyp	Ref	Expression
1		imp5.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$
2	1	imp4a	$$⊢\phi \to \left(\psi \to \left(\left(\chi \wedge \theta \right)\to \left(\tau \to \eta \right)\right)\right)$$
3	2	imp42	$$⊢\left(\left(\phi \wedge \left(\psi \wedge \left(\chi \wedge \theta \right)\right)\right)\wedge \tau \right)\to \eta$$