ODE with parameter question

Homework Statement

In a HW assignment, I'm given the ODE

$y' = f(x,y,\epsilon)$

and that $y = \phi(x,\epsilon)$is a solution to this equation.

I'm then asked, is $\phi(x,0)$ a solution to the equation

$y' = f(x,y,0)$

This result is used for the second part of the problem, and in the question I'm told I can just quote a well known theorem to explain why it's true, but I have no idea what theorem that might be. Any ideas, or maybe how to even prove it?

Since the derivative is with respect to x, not $\epsilon$, we can write $\phi(x, \epsilon)'= f(x, y, \epsilon)$ and set $\epsilon= 0$ in that equation:
$\phi(x, 0)'= f(x, y, 0)$.