How is the following statement demonstrated in 1984?John Allston: "If you don't control your mind, someone else will."
From the very beginning of this dystopian classic, Orwell stresses the way that characters like Smith have to constantly keep themselves in check to control their mind and therefore not express any hint or idea of what is really going on inside of them. Note what the reader is told about life in this strange and terrifying vision of the future in Chapter 1:
You had to live--did live, from habit that became instinct--in the assumption that every sound you made was overheard, and, except in darkness, every movement scrutinised.
Therefore, the statement quoted in the question is proved in this novel through the intense and rigorous way in which Smith is forced to police his own thoughts so as to not reveal anything about what he really thinks and feels. Even, the text goes on to say just a few lines later, a "back can be revealing." Orwell plunges us into a world where characters are constantly monitored and observed, and where the slightest deviation from what is deemed to be "acceptable" behaviour can lead to your imprisonment, torture, or worse.
Smith is engaging in a battle for his own mind, and has to struggle and fight to retain his own memories and his own sense of what is true and what is not. This is of course highlighted by his job in the ironically named Ministry of Truth, which actually supports and reinforces lies. Note what Winston tells us about the Party:
In the end the Party would announce that two and two made five, and you would have to believe it. It was inevitable that they should make that claim sooner or later: the logic of their position demanded it. Not merely the validity of experience, but the very existence of external reality was tacitly denied by their philosophy.
In this world where one day Oceania is an ally of one side and the next day it has switched allegiances and has always been the enemy of the side it was formerly allied with, Smith and others like him have to struggle to control their own mind or else abandon it to the machinations and the manipulations of the Party.