Divine Institutes 5.15:
The other part of justice, therefore, is equity; and it is plain that I am not speaking of the equity of judging well, though this also is praiseworthy in a just man, but of making himself equal to others, which Cicero calls equability. For God, who produces and gives breath to men, willed that all should be equal, that is, equally matched. He has imposed on all the same condition of living; He has produced all to wisdom; He has promised immortality to all; no one is cut off from His heavenly benefits. For as He distributes to all alike His one light, sends forth His fountains to all, supplies food, and gives the most pleasant rest of sleep; so He bestows on all equity and virtue. In His sight no one is a slave, no one a master; for if all have the same Father, by an equal right we are all children. No one is poor in the sight of God, but he who is without justice; no one is rich, but he who is full of virtues; no one, in short, is excellent, but he who has been good and innocent; no one is most renowned, but he who has abundantly performed works of mercy; no one is most perfect, but he who has filled all the steps of virtue. Therefore neither the Romans nor the Greeks could possess justice, because they had men differing from one another by many degrees, from the poor to the rich, from the humble to the powerful; in short, from private persons to the highest authorities of kings. For where all are not equally matched, there is not equity; and inequality of itself excludes justice, the whole force of which consists in this, that it makes those equal who have by an equal lot arrived at the condition of this life.
From Divine Institutes 5.16:
Some one will say, Are there not among you some poor, and others rich; some servants, and others masters? Is there not some difference between individuals? There is none; nor is there any other cause why we mutually bestow upon each other the name of brethren, except that we believe ourselves to be equal. For since we measure all human things not by the body, but by the spirit, although the condition of bodies is different, yet we have no servants, but we both regard and speak of them as brothers in spirit, in religion as fellow-servants. Riches also do not render men illustrious, except that they are able to make them more conspicuous by good works. For men are rich, not because they possess riches, but because they employ them on works of justice; and they who seem to be poor, on this account are rich, because they are not in want, and desire nothing. Though, therefore, in lowliness of mind we are on an equality, the free with slaves, and the rich with the poor, nevertheless in the sight of God we are distinguished by virtue. And every one is more elevated in proportion to his greater justice. For if it is justice for a man to put himself on a level even with those of lower rank, although he excels in this very thing, that he made himself equal to his inferiors; yet if he has conducted himself not only as an equal, but even as an inferior, he will plainly obtain a much higher rank of dignity in the judgment of God. For assuredly, since all things in this temporal life are frail and liable to decay, men both prefer themselves to others, and contend about dignity; than which nothing is more foul, nothing mere arrogant, nothing more removed from the conduct of a wise man: for these earthly things are altogether opposed to heavenly things.
This notion of equability is useful for giving practical content to the claim that all are created equal; the natural practical corollary to this is that all have a responsibility to be equable, to 'put oneself on a level even with those of lower rank' thereby to break open any rankings that spring up from the inside. The free should not merely hold as an abstract proposition that all human beings are equal; the free should make themselves equal to the slaves, putting themselves on a flat plane with them, as brothers and sisters; and so with all other mundane inequalities. The only real distinction wealth, fame, credentials, etc. bring are the ability to do great works of justice; all other distinctions are artificial and arrogant.