Matt 25:34
34 Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world:
All for whom Christ died, have a Legal Right to Eternal Life ! Jesus is here telling all for whom He died, His Sheep, those given to Him by His Father, to come, and inherit the Kingdom, which is Eternal Life !
Jesus said later Matt 25:46
And these shall go away into everlasting punishment: but the righteous into life eternal.
The Righteous are Inheriting what they had a Right to.
The word inherit in Vs 34 is the greek word klēronomeō and means:
to receive a lot, receive by lot
a) esp. to receive a part of an inheritance, receive as an inheritance, obtain by right of inheritance
b) to be an heir, to inherit
2) to receive the portion assigned to one, receive an allotted portion, receive as one's own or as a possession
3) to become partaker of, to obtain
Christ died for the Heirs of Promise. Remember Isaac ? He was an Heir, His Mother Sarah said Gal 4:30
30 Nevertheless what saith the scripture? Cast out the bondwoman and her son: for the son of the bondwoman shall not be heir with the son of the freewoman.
And Sarah was an Heir with Abraham, Isaac and Jacob Heb 11:8-
8 By faith Abraham, when he was called to go out into a place which he should after receive for an inheritance, obeyed; and he went out, not knowing whither he went.
9 By faith he sojourned in the land of promise, as in a strange country, dwelling in tabernacles with Isaac and Jacob, the heirs with him of the same promise:
This Inheritance was not earthly as many have been deceived into believing by the devil, but Heavenly Heb 11:16
16 But now they desire a better country, that is, an heavenly: wherefore God is not ashamed to be called their God: for he hath prepared for them a city.
In fact its the same Heavenly Inheritance as here 1 Pet 1:3-4
Blessed be the God and Father of our Lord Jesus Christ, which according to his abundant mercy hath begotten us again unto a lively hope by the resurrection of Jesus Christ from the dead,
4 To an inheritance incorruptible, and undefiled, and that fadeth not away, reserved in heaven for you,
Notice how it is said to be reserved in Heaven, well in the End those whom it was reserved for shall Inherit as Jesus words Matt 25:34 !
And all Believers in Christ are as Isaac was Gal 4:28
28 Now we, brethren, as Isaac was, are the children of promise.
Also Romans 9:8
That is, They which are the children of the flesh, these are not the children of God: but the children of the promise are counted for the seed.
That means all believers, whether jew or gentile were Heirs together with Abraham, Isaac and Jacob as per Heb 11:8-9
8 By faith Abraham, when he was called to go out into a place which he should after receive for an inheritance, obeyed; and he went out, not knowing whither he went.
9 By faith he sojourned in the land of promise, as in a strange country, dwelling in tabernacles with Isaac and Jacob, the heirs with him of the same promise:
Now, was Isaac born as a sinner like all of us ? Yes he was. But now was Isaac an Heir before He was born a sinner according to God's Word ? Yes he was Gen 15:3-4
3 And Abram said, Behold, to me thou hast given no seed: and, lo, one born in my house is mine heir.
4 And, behold, the word of the Lord came unto him, saying, This shall not be thine heir; but he that shall come forth out of thine own bowels shall be thine heir.
So all the Heirs of Promise are Heirs before they are even born sinners, their heirship comes from being in Union with Christ Jesus before the World began Rom 8:17
17 And if children, then heirs; heirs of God, and joint-heirs with Christ; if so be that we suffer with him, that we may be also glorified together.
Eph 1:4
4 According as he hath chosen us in him before the foundation of the world, that we should be holy and without blame before him in love:
Thats what constituted the Joint Heirship we had. For Christ was appointed Heir of all things before the World began Heb 1:2
Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds;
When was that ? It was when He became the Only Begotten Son of His Father which was before Time Began Prov 8:22-25
22 The Lord possessed me in the beginning of his way, before his works of old.
23 I was set up from everlasting, from the beginning, or ever the earth was.
24 When there were no depths, I was brought forth; when there were no fountains abounding with water.
25 Before the mountains were settled, before the hills was I brought forth or was born or begotten:
Now thats how Long the Believer, the Elect of God had a Legal Right to Eternal Life !