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Pilgrim said: But the PERSON of the Lord Jesus Christ is not Omnipresent, never was, is not now and never shall be Omnipresent. This means that the doctrine of "consubstantiation" must be rejected...
Again, I suspect that Lutherans have allowed the doctrine of "consubstantiation" to dictate their unique view of the doctrine of the Hypostatic Union. Doubtless, this is but another area of doctrine where the Reformed and Lutherans shall always differ...

All the fulness of the Godhead dwells in the undivided PERSON of the Lord Jesus Christ. The difference in teaching on the hypostatic union is the most important difference between Lutherans and Reformed and explains other doctrinal differences (e.g., sacraments, atonement).

Luther and the Lutheran Church have strongly condemned transubstantiation and consubstantiation. Let me quote the following passages from the Book of Concord. The first from Smalcald Articles was written by Luther; the second from the Formula of Concord quotes Luther.

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Of the Sacrament of the Altar we hold that bread and wine in the Supper are the true body and blood of Christ, and are given and received not only by the godly, but also by wicked Christians...As regards transubstantiation, we care nothing about the sophistical subtlety by which they teach that bread and wine leave or lose their own natural substance, and that there remain only the appearance and color of bread, and not true bread. For it is in perfect agreement with Holy Scriptures that there is, and remains, bread, as Paul himself calls it, 1 Cor. 10, 16: The bread which we break. And 1 Cor. 11, 28: Let him so eat of that bread.

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Accordingly, they hold and teach that with the bread and wine the body and blood of Christ are truly and essentially present, offered, and received. And although they believe in no transubstantiation, that is, an essential transformation of the bread and wine into the body and blood of Christ, nor hold that the body and blood of Christ are included in the bread localiter, that is, locally, or are otherwise permanently united therewith apart from the use of the Sacrament, yet they concede that through the sacramental union the bread is the body of Christ, etc. [that when the bread is offered, the body of Christ is at the same time present, and is truly tendered]. For apart from the use, when the bread is laid aside and preserved in the sacramental vessel [the pyx], or is carried about in the procession and exhibited, as is done in popery, they do not hold that the body of Christ is present....
Although this union of the body and blood of Christ with the bread and wine is not a personal union, as that of the two natures in Christ, but as Dr. Luther and our theologians, in the frequently mentioned Articles of Agreement [Formula of Concord] in the year 1536 and in other places call it sacramentatem unionem, that is, a sacramental union, by which they wish to indicate that, although they also employ the formas: in pane, sub pane, cum pane, that is, these distinctive modes of speech: in the bread, under the bread, with the bread, yet they have received the words of Christ properly...