Theorem imp5p

Description: A triple importation inference. (Contributed by Jeff Hankins, 8-Jul-2009)

	Ref	Expression
Hypothesis	3imp5.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$
Assertion	imp5p	$$⊢\phi \to \left(\psi \to \left(\left(\chi \wedge \theta \wedge \tau \right)\to \eta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		3imp5.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$
2	1	com52l	$$⊢\chi \to \left(\theta \to \left(\tau \to \left(\phi \to \left(\psi \to \eta \right)\right)\right)\right)$$
3	2	3imp	$$⊢\left(\chi \wedge \theta \wedge \tau \right)\to \left(\phi \to \left(\psi \to \eta \right)\right)$$
4	3	com3l	$$⊢\phi \to \left(\psi \to \left(\left(\chi \wedge \theta \wedge \tau \right)\to \eta \right)\right)$$