Is the ARP table dependent or independent of routing?

Hi all,

I have a question regarding the relationship between the arp table and routing.

In our network, we have a L3 link between two routers R1 and R2. If I do a show ip arp on R1 and I see R2's ip address, then does that mean that routing is established between R1 and R2? Or show ip arp doesn't really verify that routing (in this scenario, the protocol we are using is eigrp) works for a L3 link?