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Theorem bj-tagcg 33917
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 33901 . 2  |-  ( A  e.  B  <->  { A }  e. sngl  B )
2 bj-sngltag 33915 . 2  |-  ( A  e.  V  ->  ( { A }  e. sngl  B  <->  { A }  e. tag  B
) )
31, 2syl5bb 257 1  |-  ( A  e.  V  ->  ( A  e.  B  <->  { A }  e. tag  B )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    e. wcel 1767   {csn 4032  sngl bj-csngl 33897  tag bj-ctag 33906
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-v 3120  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-sn 4033  df-pr 4035  df-bj-sngl 33898  df-bj-tag 33907
This theorem is referenced by: (None)
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