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Yes, but "This do" refers to the action of partaking of the bread and wine.

"This do" refers to every aspect of the Supper. The words spoken are His words. The bread and wine are elements He has chosen and supplied through field and vineyard. We are simply beggars at His banquet where He bids us to hear His words and eat and drink His precious body and blood.

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What do you interpret the word to mean in 1 Cor. 4:1? Do you believe that Paul is referring to the apostles here, or the elders of the church, or Christians in general?

There is one office in the NT for public preaching and administering the sacraments (the mysteries) that was instituted by Christ by whatever name that office is called. Acts 20:28. Christ calls qualified men to that office to preside over churches.