You cannot prove that because it is not generally true, or because it depends on your definition of "equal loudness". Consider the case where the sound sources are inside a flaring pipe with a standing wave (say, a modified trumpet).
A standing wave is typically drawn as a standing wave of the air displacement in the pipe (illustrated), but note that the nodes of the air displacement amplitude coincide with the antinodes of the pressure amplitude.
The sound sources (say, small piezo loudspeakers) are pressure transducers and they are placed at the antinodes of the pressure amplitude. If each of them contributes to a fixed pressure amplitude $\Delta p$ at the position of the listener, then $N$ of these pressure transducers ($N=7$ in the picture) will produce $7\Delta p$ of pressure amplitude and $N^2=49$ times more acoustic energy compared to a single transducer.
(Update: I assumed that the sound source primarily act on pressure. It might be more appropriate to consider sound sources as acting on air displacement, in which case they should be placed at the antinodes; the reasoning is otherwise similar.)
How is this possible? Where does the energy come from? Rest assured: the law of energy conservation is not violated. In a case like this, where the acoustic sources can feel each other, the sources have to work harder in order to achieve the same pressure. Imagine that you are driving a damped harmonic oscillator. If you put in twice as much amplitude, you get twice as much amplitude out, but you need to put in four times more power.
Now, if you say that each sound source adds a fixed amount of acoustic power, rather than a fixed amount of amplitude, then your statement is automatically true because of energy conservation. For a case like an ensemble of singers or musical instruments, the coupling between the sound sources is so weak that the difference between sources of fixed amplitude and sources of fixed power is negligible. But if you design a loudspeaker line array for use in churches or train stations, with the purpose of radiating the sound horizontally and not vertically, then this distinction will not be negligible and must be taken into account.