"It" versus "that"

I wrote:

Generally, the tangent of the sum of several angles is given by [insert formula here]. That is proved by an easy induction on n once one has the case of two angles.

Some sort of copyeditor changed "That" to "It":

Generally, the tangent of the sum of several angles is given by [insert formula here]. It is proved by an easy induction on n once one has the case of two angles.

My efforts to correct a gross error by the copyeditor (or whatever they were) elsewhere in the paper distracted me from the issue of the merits or demerits of that particular change, and the paper was published with "it" instead of "that." Hardly a disaster, but I am not as comfortable with "it" as with "that."

Am I right or am I being too nitpicking?

“It” as a pronoun is not uniquely defined by the first sentence. Does it refer to the tangent, the sum, or to the giving that is implied by the sentence? The copyeditor has obscured your meaning.

“That”, as a demonstrative referring to that which has gone before, has a much clearer meaning, because it can only refer to the assertion made by the whole of the first sentence.

This or that (by either of which I refer demonstratively to the whole notion of my preceding paragraph) justifies your scepticism about the copyeditor.