Give a statement of the standard axioms for group theory:

Find supertheories of group theory:

This is Wolfram's shortest possible axiom for Boolean algebra:

By default, the axiom uses CenterDot to format the binary operator used:

Return the axiom using your own named operator:

Prove commutativity of the operator:

Give a list of currently supported axiomatic theories:

Give a list of currently supported properties about axiomatic theories:

Get the axioms of a theory, using default names for its operators:

AxiomaticTheory[theory] also gives the axioms of the theory:

These are the default operator names used by the group axioms in AxiomaticTheory:

Specify your own operator names using an association:

Specify only the name of the inversion operation:

Find the arities of the operators of an axiomatic theory:

Get the same arities for the same theory with your own specification of operator names:

Get notable theorems of Boolean algebra:

Get a dataset of information about the following:

Show the named axioms:

List the authors of a theory:

Year of formulation:

Bibliographical citation:

Take the axioms of Boolean logic in this form:

Get the arities of the operators of the theory:

Construct all formulas containing the same free variable twice:

Select which of those formulas is equivalent to the free variable itself:

Get the axioms of group theory and the generating relations for the quaternion group, generated by i, j:

Prove that the fourth power of both generators is the identity element:

If theory₁ is a subtheory of theory₂, then theory₂ is a supertheory of theory₁:

Equivalent theories of theory are not considered subtheories nor supertheories of theory:

The axioms of a subtheory can be proven from those of a supertheory using the same operators:

However, not all theorems of the supertheory can be proven from those of the subtheory: