Theorem iprc

Description: The identity function is a proper class. This means, for example, that we cannot use it as a member of the class of continuous functions unless it is restricted to a set, as in idcn . (Contributed by NM, 1-Jan-2007)

	Ref	Expression
Assertion	iprc	|- -. _I e. _V

Proof

Step	Hyp	Ref	Expression
1		dmi	|- dom _I = _V
2		vprc	|- -. _V e. _V
3	1 2	eqneltri	|- -. dom _I e. _V
4		dmexg	|- ( _I e. _V -> dom _I e. _V )
5	3 4	mto	|- -. _I e. _V