The connection of his blood with ‘the (new) covenant’ is another aspect of the Exodus theme. After the Exodus, God made Israel his own people by making a covenant with them, and the covenant was sealed with the blood of sacrificed oxen, called ‘the blood of the covenant’. In the book of Jeremiah the prophet, God promised ‘a new covenant’, one that would transcend the people’s disobedience to the first covenant.
