The worst problem with using equality in this way is that equality on propositions doesn't have a single meaning. Originally, in Boole's logic, it meant that one formula was obtained from another by a series of algebraic manipulations. Now, it might mean that the formulae belong to the same equivalence class in the Lindenbaum algebra of a logic.
The problem is that these two differ. One might have a theory of algebraic manipulations on formulae that is decidable for a logic that is undecidable: it is not rare in proof theory to say that two formulae are equal iff they have the same negation normal form, for instance, which isan algebraic notion of equality using just De Morgan duality and that negation is involutive. Then equality and logical equivalence do not coincide, as they must with the second interpretation.
Feel free to use equality on propositions if you wish, but do make clear what you are doing. If you follow Amy's advice, there is no need to spell this out.