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Definition df-nul 4292
 Description: Define the empty set. More precisely, we should write "empty class". It will be posited in ax-nul 5203 that an empty set exists. Then, by uniqueness among classes (eq0 4308, as opposed to the weaker uniqueness among sets, nulmo 2798), it will follow that ∅ is indeed a set (0ex 5204). Special case of Exercise 4.10(o) of [Mendelson] p. 231. For a more traditional definition, but requiring a dummy variable, see dfnul2 4293. (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
StepHypRef Expression
1 c0 4291 . 2 class
2 cvv 3495 . . 3 class V
32, 2cdif 3933 . 2 class (V ∖ V)
41, 3wceq 1533 1 wff ∅ = (V ∖ V)
 Colors of variables: wff setvar class This definition is referenced by:  dfnul2  4293  dfnul2OLD  4294  noel  4296  noelOLD  4297
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