Interesting, that it's not what Jer 31 says...
Jeremiah 31:31 KJV
Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah:
Is the church the house of Israel or the house of Judah?
In its immediate application to the first audience, this could be applied to the renewal of the covenant that was broken and resulted in the residents of Judah, including Jeremiah, being taken into captivity in Babylon. In Daniel we see Daniel referring to the prophecy of Jeremiah that promised a restoration and return after seventy years. Prophecy in the OT often has more than one fulfillment, some partial, until the final fulfillment. So we have to look at the things the New Testament says about the same prophecy to find that. I showed you where Paul did just that. OT prophecy is not read literalisticly and is read uniquely to other forms of writing. It is not historical narrative of future events. There is a whole key to interpreting OT prophecy, but I am not going to be your teacher on the matter, as my qualifications to do so are limited. It is something every serious Bible student should learn. Otherwise assumptions will be made, misinterpretations presented as correct, and in the case of making them exclusively about the geo/political/ethnic, divide peoples and redemption. Which the NT clearly does not do.
This should not mean that the Old Testament prophecies given to Israel are null and void,
It doesn't. That is a false equivalency.
as an example, how did Jesus fulfill...
Jeremiah 31:35-37 KJV
Thus saith the LORD, which giveth the sun for a light by day, and the ordinances of the moon and of the stars for a light by night, which divideth the sea when the waves thereof roar; The LORD of hosts is his name: [36] If those ordinances depart from before me, saith the LORD, then the seed of Israel also shall cease from being a nation before me for ever. [37] Thus saith the LORD; If heaven above can be measured, and the foundations of the earth searched out beneath, I will also cast off all the seed of Israel for all that they have done, saith the LORD.
Let's look at it from the perspective of what we find in the NT.
We find a New Covenant'
We find the OC being made obsolete by the new.
So we must establish what a covenant is so we can move forward through the passage. A covenant is a relationship, in this case, God with man. Those he, and he alone, bring into that covenant are his people. The covenant he made with Jacob's (Israel) descendants, makes them his people. Those he brings into the New Covenant are his people. Those in the NC are not restricted by national or ethnic boundaries as they were in the OC. (Don't forget, the whole world belongs to God.)
What else do we find in the NT?
In Romans 9:6 we find ("not all who are descended from Israel belong to Israel")
In Gal 3:29 ("if you are Christ's, then you are Abraham's offspring").
The passage ultimately speaks of the Chruch as the continuation and fulfillment of Israel---not a replacement, but the expansion of God's covenant people.
The prophecy was given by a Jew and to Jews who did not know what we now know. Therefore it is worded according to Jewish understanding of God's people. They did not know about the work of Christ to bring about the Church. God feels the same way about believing Jews as he does about believing Gentiles. They are his people.
Hosea 2:23
and I will show her for myself in the land, And I will have mercy on No Mercy, and I will say to Not My People, 'You are my people'; and he shall say, 'You are my God.""
If the Church (physical and spiritual Israel) has replaced Israel, then this promise is not true.
See above. The Church does not replace Israel.
No one present today was part of the original audience. Therefore, are any promises for us today?
Another false equivalency. That is not the only option and it is obviously untrue. The very passage you quote from Jer 31 and asked about, guarantees that the covenant promise will come to pass by it use of things of nature that are fixed and certain.
