ProofCheck is a system for writing and checking mathematical proofs. Theorems and proofs are contained in a plain {\TeX} or {\LaTeX} document. Parsing and proof checking are accomplished through Python programs which read the source file. A general explanation of the use and structure of the system and programs is provided and a sample proof is shown in detail. The work done by the authors has been based on standard sentence logic, a non-standard predicate logic and set theory with proper classes. Theorems and proofs based on other foundations may be checked if external data files are modified. Four such data files and their possible modifications are described. In addition, the extent to which the formal language can be shaped to accommodate an author's preferences is discussed.