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Theorem bj-0eltag 34956
Description: The empty set belongs to the tagging of a class. (Contributed by BJ, 6-Apr-2019.)
Assertion
Ref Expression
bj-0eltag  |-  (/)  e. tag  A

Proof of Theorem bj-0eltag
StepHypRef Expression
1 0ex 4569 . . . . 5  |-  (/)  e.  _V
21snid 4044 . . . 4  |-  (/)  e.  { (/)
}
32olci 389 . . 3  |-  ( (/)  e. sngl  A  \/  (/)  e.  { (/)
} )
4 elun 3631 . . 3  |-  ( (/)  e.  (sngl  A  u.  { (/)
} )  <->  ( (/)  e. sngl  A  \/  (/)  e.  { (/) } ) )
53, 4mpbir 209 . 2  |-  (/)  e.  (sngl 
A  u.  { (/) } )
6 df-bj-tag 34953 . 2  |- tag  A  =  (sngl  A  u.  { (/)
} )
75, 6eleqtrri 2541 1  |-  (/)  e. tag  A
Colors of variables: wff setvar class
Syntax hints:    \/ wo 366    e. wcel 1823    u. cun 3459   (/)c0 3783   {csn 4016  sngl bj-csngl 34943  tag bj-ctag 34952
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432  ax-nul 4568
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2651  df-v 3108  df-dif 3464  df-un 3466  df-nul 3784  df-sn 4017  df-bj-tag 34953
This theorem is referenced by:  bj-tagn0  34957
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