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Basically, the difference between the Thomistic notion of transubstantiation and the interpretation of Lutherans and Anglicans is that those who hold to the doctrine of transubstantiation believe that after the consecration, the "substance" of what was the bread is replaced by the substance of Jesus, while the "accidents" of the bread remain,so the host looks tastes, feels, smells, and reacts like bread, but is not.
By contrast, those who hold to consubstantiation, say that Jesus is present, just as those who subscribe to transubstantiation believe, but that this occurs by Jesus becoming really present in substance at the same time the substance of the bread is.
Some of those who believe in consubstantiation note that there is a problem reconciling yransubstantiation with John 6:48, wherein it is recorded that Jesus states:
I am the bread of life
and John 6:51a, wherein it is recorded that Jesus states:
I am the living bread which came down from heaven ...
Now, if Jesus is living bread, how can it be that after transubstantiation, that there is no substance of bread present, as Jesus is bread.