Shall be saved by His Life !
Rom 5:10
10 For if, when we were enemies, we were reconciled to God by the death of his Son, much more, being reconciled, we shall be saved by his life.
Another reason why it is a myth to say that Christ died for all without exception, is because all He died for shall be saved by His Life..
And we know that all without exception shall be saved. For many shall perish in their sins.
What many in man made religion do not understand about the Work of Christ, that it is also Christ responsibility as Saviour of God's People, that what He did on the cross is applied to all He died to save, and that's why its stated after His resurrection that He went to appear before God for us Heb 9:24
24 For Christ is not entered into the holy places made with hands, which are the figures of the true; but into heaven itself, now to appear in the presence of God for us:
The us here are the elect of God, The many sons He brings to Glory, the seed of Abraham, the children God gave Him, partakers of the Heavenly calling.
Now a major reason for this [His appearing for us], is that as part of His Saving Purpose, He is to make intercession [for application] for all those He died. The Lord Jesus Christ intercessory work is vital for the applying of all His saving benefits to God's elect. There is an efficacy in His intercession, this is True because of His Merit and therefore shall prevail with God.
The Holy Spirit is vital in answering the call here, and is the Gift that the Father gave to the Son for His cross work Acts 2:33
33Therefore being by the right hand of God exalted, and having received of the Father the promise of the Holy Ghost, he hath shed forth this, which ye now see and hear.
And because we shall saved by His Life, The Holy Spirit communicates to all of God's elect, those Christ died for, the Life we have in Christ as He is our risen Head and Mediator, Hence as it is written, the Gift of God is eternal life through Jesus Christ our Lord, and the meritorious ground whereby the Spirit imparts life to dead elect sinners is the work or cross of Christ...
All men without exception do not receive this life, because Christ did not die for them who do not receive it.