Equivalence classes in completness proof of predicate logic

Question

I am reading Henkin style proof of completeness of predicate logic. In the proof, the language includes an equality symbol ($\equiv$). I remember reading here that equality symbol is optional. The way this is handled in the proof is by redefining the symbol set using the equivalence class defined by the equality relation. I have two questions 1. Why is this symbol optional? 2. If it is removed, how would it affect the proof?