This site has explanations of concepts at work in mathematical logic
and the Prooftoys system, with interactive pictures like these:
Move on to:
The logic of Prooftoys, and logical inference.
Proofs about logic and the real numbers. Understand in detail or just browse.
Building your own proofs with the online proof builder. This tool has some rough edges still, but don’t worry; it will only do correct inferences.
A more finished version of the proof builder is targeted for solving simple equations, at the companion Mathtoys site.