And known have the house of Israel that I am Jehovah their God, From that day and henceforth.

So the children of Israel will be certain that I am the Lord their God, from that day and for the future.

And the house of Israel shall know that I am the Lord, their God, from that day and thereafter.

So the house of Israel shall know that I am the Lord their God,.... That has chosen them, redeemed them, called them, manifested his covenant love and grace to them, and protected and defended them: this destruction of their enemies will be a proof of it; and they will hereby be led into a clearer knowledge of him, and of his goodness to them; and make a more firm and constant profession of him,
even from that day and forward, to the end of time; for after this the Jews will no more apostatize, but will for ever remain the people of God and Christ.

So the house of Israel shall know . . . Lord--by My interposition for them. So, too, the heathen shall be led to fear the name of the Lord (Psalm 102:15).