Theorem dfnul4

Description: Alternate definition of the empty class/set. (Contributed by BJ, 30-Nov-2019) Avoid ax-8 , df-clel . (Revised by Gino Giotto, 3-Sep-2024)

	Ref	Expression
Assertion	dfnul4	|- (/) = { x | F. }

Proof

Step	Hyp	Ref	Expression
1		dfnul2	|- (/) = { x | -. x = x }
2		equid	|- x = x
3	2	notnoti	|- -. -. x = x
4	3	bifal	|- ( -. x = x <-> F. )
5	4	abbii	|- { x | -. x = x } = { x | F. }
6	1 5	eqtri	|- (/) = { x | F. }