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Theorem bj-tagci 35733
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-tagci (𝐴𝐵 → {𝐴} ∈ tag 𝐵)

Proof of Theorem bj-tagci
StepHypRef Expression
1 bj-snglc 35718 . 2 (𝐴𝐵 ↔ {𝐴} ∈ sngl 𝐵)
2 bj-sngltagi 35731 . 2 ({𝐴} ∈ sngl 𝐵 → {𝐴} ∈ tag 𝐵)
31, 2sylbi 216 1 (𝐴𝐵 → {𝐴} ∈ tag 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  {csn 4623  sngl bj-csngl 35714  tag bj-ctag 35723
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-11 2154  ax-12 2171  ax-ext 2703  ax-sep 5293  ax-pr 5421
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-rex 3071  df-v 3476  df-un 3950  df-in 3952  df-ss 3962  df-sn 4624  df-pr 4626  df-bj-sngl 35715  df-bj-tag 35724
This theorem is referenced by: (None)
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