Consider the theory with the following axioms:

* The axioms of ZFC
* The "axiom of consistency": "This theory, including this axiom and all of the theory's other axioms, is consistent." Phrased differently (and equivalently):

	+ This theory does not prove $\text{False}$
	+ This theory states its own consistency as an axiom.

Can one have such a theory, one that includes its own consistency as an axiom? Can this theory be consistent?