Megill M. Metamath. A Computer Language for Mathematical Proofs 2019

Textbook in PDF format

Metamath is a computer language and an associated computer program for archiving, verifying, and studying mathematical proofs at a very detailed
level. The Metamath language incorporates no mathematics per se but treats all mathematical statements as mere sequences of symbols.You provide
Metamath with certain special sequences (axioms) that tellit what rules of inference are allowed. Metamath is not limited to any specific field of
mathematics. The Metamath language is simple and robust, with an almost total absence of hard-wired syntax, and we1 believe that it provides about
the simplest possible framework that allows essentially all of mathematics to be expressed with absolute rigor.
Using the Metamath language, you can build formal or mathematical systems2 that involve inferences from axioms. Although a database is provided that includes a recommended set of axioms for standard mathematics, if you wish you can supply your own symbols, syntax, axioms, rules, and
definitions.
The name “Metamath” was chosen to suggest that the language provides a means for describing mathematics rather than being the mathematics itself. Actually in some sense any mathematical language is metamathematical. Symbols written on paper, or stored in a computer, are not mathematics itself but rather a way of expressing mathematics.For example “7” and “VII” are symbols for denoting the number seven in Arabic and Roman numerals; neither is the number seven