Did Jesus successfully accomplish His mission in coming to Earth?

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He expanded the family of God from being exclusively Israel to including everyone on earth – through the work of the Cross.
Ephesians 2:14-18

14 For He Himself is our peace, who has made both one, and has broken down the middle wall of separation,
15 having abolished in His flesh the enmity, that is, the law of commandments contained in ordinances, so as to create in Himself one new man from the two, thus making peace,
16 and that He might reconcile them both to God in one body through the cross, thereby putting to death the enmity.
17 And He came and preached peace to you who were afar off and to those who were near.
18 For through Him we both have access by one Spirit to the Father (NKJV).

2. He removed our sin and disarmed the Devil.
Colossians 2:13-15
13 And you, being dead in your trespasses and the uncircumcision of your flesh, He has made alive together with Him, having forgiven you all trespasses,
14 having wiped out the handwriting of requirements that was against us, which was contrary to us. And He has taken it out of the way, having nailed it to the cross.
15 Having disarmed principalities and powers, He made a public spectacle of them, triumphing over them in it (NKJV).

3. He reconciled the universe back to God.
Colossians 1:19,20
19 For it pleased the Father that in Him all the fullness should dwell,
20 and by Him to reconcile all things to Himself, by Him, whether things on earth or things in heaven, having made peace through the blood of His cross (NKJV).

4. He saves, heals, and delivers all of those who come to Him and the Father, taking them from the gutter-most to the uttermost.

Hebrews 7:24,25
24 But He, because He continues forever, has an unchangeable priesthood.
25 Therefore He is also able to save to the uttermost those who come to God through Him, since He always lives to make intercession for them (NKJV).

5. Through the Cross, Jesus destroyed the works of the Devil and made perfect righteousness available to our spirits.
1 John 3:7-9
7 Little children, let no one deceive you. He who practices righteousness is righteous, just as He is righteous.
8 He who sins is of the devil, for the devil has sinned from the beginning. For this purpose the Son of God was manifested, that He might destroy the works of the devil.
9 Whoever has been born of God does not sin, for His seed remains in him; and he cannot sin, because he has been born of God (NKJV).

6. He gave us the ability to remember and receive His benefits of salvation and healing.
Psalm 103:1-3
1 Bless the LORD, O my soul; And all that is within me, bless His holy name!
2 Bless the LORD, O my soul, And forget not all His benefits:
3 Who forgives all your iniquities, Who heals all your diseases (NKJV).

7. He became the Lord, Our Physician and Healer (Jehovah Rapha) by His victory over death, hell, and the grave.
Exodus 15:26 –“If you diligently heed the voice of the LORD your God and do what is right in His sight, give ear to His commandments and keep all His statutes, I will put none of the diseases on you which I have brought on the Egyptians. For I am the LORD who heals you”(NKJV).