Was it stated in any one of the universal councils before the schism in 1054 that the One Universal Church is defined by Eucharist? I mean a statement that if the Eucharist is not practiced in a certain Christian group than this group is not a part of the Church.
The general rule of the Councils is that they are created out of a great crisis in the Church. This could be either theological (as in the first seven), or political (the healing of the Great Western Schism). While the identification of the eucharist with the body and blood of Christ can be seen in both the East and the West prior to the split, the first major challenges (there had been a minor challenge while the Church was united, but that never gained real traction) to the doctrine were only felt immediately after the schism (literally, within the same decade).
A couple of related thoughts:
- One can only wonder if the anti-eucharistic theology had gotten traction earlier if the resulting Council would have helped prevent the schism.
- Vatican II was the only Council which was not created at a definitive time of crisis. Interesting to think about at least.
- While the major crises of the East were resolved by Councils, Manichaeism and Donatism really never had a presence in the East. Those two heresies had a profound impact on Western theology. That is one reason why there is a difference between how Catholics and Orthodox view who is appropriate minister of Baptism (Catholic = anyone, clergy preferable; Orthodox = clergyman only).