The following words from St Cyril of Alexandria address the victory Our Lord achieved for mankind by His fasting and temptation.
[The Lord] arose and helped [us], having taken the form of a slave, and being made in the likeness of men: for so did He as one of us set Himself as an avenger in our stead, against that murderous and rebellious serpent, who had brought sin upon us, and thereby had caused corruption and death to reign over the dwellers upon earth, that we by His means, and in Him, might gain the victory, whereas of old we were vanquished, and fallen in Adam.
Come therefore and let us praise the Lord, and sing psalms unto God our Saviour: let us trample Satan under foot; let us raise the shout of victory over him now he is thrown and fallen: let us exult over the crafty reptile, caught in an inextricable snare: let us too say of him in the words of the prophet Jeremiah, “How is the hammer of all the earth broken and beaten small! Thou art found and hast been taken, because thou stoodest against the Lord.” For of old, that is before the time of the advent of Christ the Saviour of all, the universal enemy had somewhat grand and terrible notions about himself: for he boastfully exulted over the infirmity of the inhabitants of the earth, saying, “I will hold the world in my hand as a nest, and as eggs that are left I will take it up: and no one shall escape from me or speak against me.” And in very truth there was no one of those upon earth who could rise up against his power; but the Son rose up against him, and contended with him, having been made like unto us. And therefore, as I said, human nature, as victorious in Him, wins the crown. And this in old time the Son Himself proclaimed, where by one of the holy prophets He thus addresses Satan; “Behold, I am against thee, O corrupting mountain, that corruptest the whole earth.”