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Theorem bj-tagcg 31328
Description: Characterization of the elements of  B in terms of elements of its tagged version. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
bj-tagcg  |-  ( A  e.  V  ->  ( A  e.  B  <->  { A }  e. tag  B )
)

Proof of Theorem bj-tagcg
StepHypRef Expression
1 bj-snglc 31312 . 2  |-  ( A  e.  B  <->  { A }  e. sngl  B )
2 bj-sngltag 31326 . 2  |-  ( A  e.  V  ->  ( { A }  e. sngl  B  <->  { A }  e. tag  B
) )
31, 2syl5bb 260 1  |-  ( A  e.  V  ->  ( A  e.  B  <->  { A }  e. tag  B )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187    e. wcel 1870   {csn 4002  sngl bj-csngl 31308  tag bj-ctag 31317
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-9 1874  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407  ax-sep 4548  ax-nul 4556  ax-pr 4661
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ne 2627  df-ral 2787  df-rex 2788  df-v 3089  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-sn 4003  df-pr 4005  df-bj-sngl 31309  df-bj-tag 31318
This theorem is referenced by: (None)
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