You must be confused. Darby also taught the premill doctrine.
Matthew 25:31-46 leaves no mortals alive on the planet after the Second Coming of Christ.
The "time of the judgment of the dead" is found in Revelation 11:18, right after the 7th trumpet, which is the last trumpet in the Bible.
The fire comes at the Second Coming of Christ in 2 Thessalonians 1:7-10.
The fire also comes at the end of Revelation chapter 20.
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We get a little deeper here, it is up to you whether you will ponder these things a little more or whether you will simply wave the hand.
Darby preached a pre tribulation rapture which is not only wrong in substance but crooked in the way he set about proving his doctrine i.e he deliberately set out to deceive,
He knew apostasis does not mean departure from one place to another or removal, he was an Oxford educated theologian and could not have been mistaken, so he was being crooked.
The word in 2.Thess.2 is rebellion, a departure from the faith, the church in 70ad was still multiplying at a phenominal rate, millions were turning to the Lord and in all ranks and status of life.
Also Darby did notice those great and wonderful promises God made to the Jews in every book of prophecy Micah.4. for e.g. "it shall come to pass in the latter days...." and quite rightly he concluded that these promises could never belong to the church.
But in the last days it shall come to pass that the mountain of the house of the Lord shall be established in the top of the mountains and shall be exalted above the hills and people shall flow into it.
And many nations shall come and say "come and let us go up to the mountain of the Lord and to the house of the God of Jacob and He will teach us His ways and we will walk in His paths" for the law shall go forth of Zion and the word of the Lord from Jerusalem.
And He shall judge among many people and rebuke strong nations afar off and they shall beat their swords into ploughshares and their spears into pruning hooks nation shall not lift up sword against nation neither shall they learn war any more.
But they shall sit every man under his vine and under his fig tree and none shall make them afraid
for the mouth of the Lord hath spoken it.
This is taken from Isaiah. It comprises the great Jewish hope, it is what they understood as the Kingdom of God, it is what they believed in and expected...when Jesus came preaching the Kingdom of God is nigh they pricked up their ears.
Darby rightly recognised that these promises are the OPPOSITE to what Jesus taught the church to expect.
The world was not to come to us, we were to go to the world. Nations would lift up sword against nation and wars would continue and increase right up to His return. People would not sit under their vine and their fig tree but there would be disaster and famine.
But for some odd reason known only to Darby he concluded from this that Israel [which at that time was not a nation] would go through the tribulation...looks to me like they are in safety and peace and prosperity...but that is that.
Now Isaiah and Micah are not alone in teaching this prophecy for the latter days, it is what every Jew believed...they ALL taught it....they still do.
It has not come to pass.....it MUST then be still future..