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Theorem bj-df-nul 33542
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 3784 . . 3  |-  -.  x  e.  (/)
21bifal 1387 . 2  |-  ( x  e.  (/)  <-> F.  )
32bj-abbi2i 33320 1  |-  (/)  =  {
x  | F.  }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1374   F. wfal 1379    e. wcel 1762   {cab 2447   (/)c0 3780
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1963  ax-ext 2440
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1377  df-fal 1380  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2612  df-v 3110  df-dif 3474  df-nul 3781
This theorem is referenced by: (None)
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