Right, and there is more than that.
The Body of Christ, (the body of his teaching) is made entirely of the words that Jesus received from God like manna from heaven which became his flesh, his teaching, a new metaphor for divine instruction.. John 6:63
This is the only way that Jesus can be in you and with you, if the body of his teaching from God is in you then he is in you and you are in him as he is in and with God and God is in and with him, united by one teaching, one truth, one light, and one way to follow the law that leads to eternal life.
"And the glory which You gave Me I have given them, that they may be one just as We are one: I in them, and You in Me; that they may be perfectly one, that the world may know that You have sent Me,"
To eat the body of Christ is to receive the teaching of Jesus, revealed to him by God, about the figurative nature of the words in the law and hidden subjects. To drink his blood is to do it.