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Theorem bj-tagci 34381
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 34366 . 2 (𝐴𝐵 ↔ {𝐴} ∈ sngl 𝐵)
2 bj-sngltagi 34379 . 2 ({𝐴} ∈ sngl 𝐵 → {𝐴} ∈ tag 𝐵)
31, 2sylbi 220 1 (𝐴𝐵 → {𝐴} ∈ tag 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2114  {csn 4539  sngl bj-csngl 34362  tag bj-ctag 34371
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 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-11 2161  ax-12 2178  ax-ext 2794  ax-sep 5179  ax-nul 5186  ax-pr 5307
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-nfc 2962  df-rex 3136  df-v 3471  df-dif 3911  df-un 3913  df-in 3915  df-ss 3925  df-nul 4266  df-sn 4540  df-pr 4542  df-bj-sngl 34363  df-bj-tag 34372
This theorem is referenced by: (None)
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