Definition df-nul 4255

Description: Define the empty set. More precisely, we should write "empty class". It will be posited in ax-nul 5223 that an empty set exists. Then, by uniqueness among classes (eq0 4275, as opposed to the weaker uniqueness among sets, nulmo 2715), it will follow that ∅ is indeed a set (0ex 5224). Special case of Exercise 4.10(o) of [Mendelson] p. 231. For a more traditional definition, but requiring a dummy variable, see dfnul2 4257. (Contributed by NM, 17-Jun-1993.) Clarify that at this point, it is not established that it is a set. (Revised by BJ, 22-Sep-2022.)

Assertion

Ref	Expression
df-nul	⊢ ∅ = (V ∖ V)

Detailed syntax breakdown of Definition df-nul

Step	Hyp	Ref	Expression
1		c0 4254	. 2 class ∅
2		cvv 3423	. . 3 class V
3	2, 2	cdif 3881	. 2 class (V ∖ V)
4	1, 3	wceq 1543	1 wff ∅ = (V ∖ V)

This definition is referenced by:  dfnul4  4256  dfnul2OLD  4259  noelOLD  4263