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Definition df-nul 4142
Description: Define the empty set. More precisely, we should write "empty class". It will be posited in ax-nul 5027 that an empty set exists. Then, by uniqueness among classes (eq0 4157, as opposed to the weaker uniqueness among sets, nulmo 2761), it will follow that is indeed a set (0ex 5028). Special case of Exercise 4.10(o) of [Mendelson] p. 231. For a more traditional definition, but requiring a dummy variable, see dfnul2 4143. (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.)
Ref Expression
df-nul ∅ = (V ∖ V)

Detailed syntax breakdown of Definition df-nul
StepHypRef Expression
1 c0 4141 . 2 class
2 cvv 3398 . . 3 class V
32, 2cdif 3789 . 2 class (V ∖ V)
41, 3wceq 1601 1 wff ∅ = (V ∖ V)
Colors of variables: wff setvar class
This definition is referenced by:  dfnul2  4143  dfnul2OLD  4144  noel  4146  noelOLD  4147
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