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Theorem bj-df-nul 31132
Description: Alternate definition of the empty class/set. (Contributed by BJ, 30-Nov-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-df-nul  |-  (/)  =  {
x  | F.  }

Proof of Theorem bj-df-nul
StepHypRef Expression
1 noel 3739 . . 3  |-  -.  x  e.  (/)
21bifal 1416 . 2  |-  ( x  e.  (/)  <-> F.  )
32bj-abbi2i 30909 1  |-  (/)  =  {
x  | F.  }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1403   F. wfal 1408    e. wcel 1840   {cab 2385   (/)c0 3735
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650  ax-5 1723  ax-6 1769  ax-7 1812  ax-10 1859  ax-11 1864  ax-12 1876  ax-13 2024  ax-ext 2378
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1406  df-fal 1409  df-ex 1632  df-nf 1636  df-sb 1762  df-clab 2386  df-cleq 2392  df-clel 2395  df-nfc 2550  df-v 3058  df-dif 3414  df-nul 3736
This theorem is referenced by: (None)
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