In his Analysis I book, Terence Tao defines two functions $f,g:X\to Y$ to be equal if $f(x)=g(x)$, for all $x\in X$. After giving some examples of this concept, he then says:
This notion of equality obeys the usual axioms (Exercise 3.3.1).
It is quite easy to show that this relation defined on the class of functions is reflexive, symmetric, and transitive. But how do one verify that the substitution property is satisfied too?