One reason Russia has been supporting euroskeptic movements across Europe is that they’re anti-American. A rift between the EU and the U.S. would be useful to Putin for more than just the easing of sanctions: It would weaken what the Russian president views as an existential threat to his regime from the U.S.

It’s far from certain, however, that the U.S. ‘s influence in Europe will wane. There are other U.S.-oriented nations in the union: Poland and the Baltic states are examples, and even Germany. The U.K. remains a member of the North Atlantic Treaty Organization along with most EU members. The U.K.’s exit is no reason for the rest of Europe to become more anti-American — unless it gives rise to more euroskeptic electoral successes and a greater representation in parliaments for Putin’s allies.

That assumes EU leaders will do nothing to fix the union. There is still a chance that they will react to Brexit by shoring up the organization and that the nucleus, its founding members, will try to save the European dream. If the EU becomes more cohesive without the U.K., which often pulled in the other direction, and if the U.S. plays a role, Brexit may end up being a setback for Putin’s foreign policy goals.

Both the immediate matter of sanctions and the long-term state of the EU, as well as its relationship with the U.S., never depended on the U.K. as much as on Europe’s continental powers.