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Theorem bj-tagcg 34818
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 34802 . 2 (𝐴𝐵 ↔ {𝐴} ∈ sngl 𝐵)
2 bj-sngltag 34816 . 2 (𝐴𝑉 → ({𝐴} ∈ sngl 𝐵 ↔ {𝐴} ∈ tag 𝐵))
31, 2syl5bb 286 1 (𝐴𝑉 → (𝐴𝐵 ↔ {𝐴} ∈ tag 𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wcel 2114  {csn 4516  sngl bj-csngl 34798  tag bj-ctag 34807
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-11 2162  ax-12 2179  ax-ext 2710  ax-sep 5167  ax-nul 5174  ax-pr 5296
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-tru 1545  df-fal 1555  df-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-rex 3059  df-v 3400  df-dif 3846  df-un 3848  df-in 3850  df-ss 3860  df-nul 4212  df-sn 4517  df-pr 4519  df-bj-sngl 34799  df-bj-tag 34808
This theorem is referenced by: (None)
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