Theorem dfatprc

Description: A function is not defined at a proper class. (Contributed by AV, 1-Sep-2022)

	Ref	Expression
Assertion	dfatprc	|- ( -. A e. _V -> -. F defAt A )

Proof

Step	Hyp	Ref	Expression
1		prcnel	|- ( -. A e. _V -> -. A e. dom F )
2	1	orcd	|- ( -. A e. _V -> ( -. A e. dom F \/ -. Fun ( F |` { A } ) ) )
3		ianor	|- ( -. ( A e. dom F /\ Fun ( F |` { A } ) ) <-> ( -. A e. dom F \/ -. Fun ( F |` { A } ) ) )
4		df-dfat	|- ( F defAt A <-> ( A e. dom F /\ Fun ( F |` { A } ) ) )
5	3 4	xchnxbir	|- ( -. F defAt A <-> ( -. A e. dom F \/ -. Fun ( F |` { A } ) ) )
6	2 5	sylibr	|- ( -. A e. _V -> -. F defAt A )