For a few other examples, you can look at the subsection "126.96.36.199 Complex numbers (supplements)" (beginning with ~bj-subcom), in my mathbox. They are in deduction form and for most of them, the conclusion is an equivalence. There are a few other algebraic lemmas in other mathboxes as well. In my case, I haven't tried to be systematic and haven't thought too much about the most economical way to treat these, but I used some of them to prove a formula for barycentric coordinates in ~bj-bary1.
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