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Theorem bj-tagcg 36497
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 (𝐴𝑉 → (𝐴𝐵 ↔ {𝐴} ∈ tag 𝐵))

Proof of Theorem bj-tagcg
StepHypRef Expression
1 bj-snglc 36481 . 2 (𝐴𝐵 ↔ {𝐴} ∈ sngl 𝐵)
2 bj-sngltag 36495 . 2 (𝐴𝑉 → ({𝐴} ∈ sngl 𝐵 ↔ {𝐴} ∈ tag 𝐵))
31, 2bitrid 282 1 (𝐴𝑉 → (𝐴𝐵 ↔ {𝐴} ∈ tag 𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wcel 2098  {csn 4632  sngl bj-csngl 36477  tag bj-ctag 36486
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-11 2146  ax-12 2166  ax-ext 2699  ax-sep 5303  ax-pr 5433
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-rex 3068  df-v 3475  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4327  df-sn 4633  df-pr 4635  df-bj-sngl 36478  df-bj-tag 36487
This theorem is referenced by: (None)
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