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Metamath Proof Explorer

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