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Theorem bj-tagci 36371
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 36356 . 2 (𝐴𝐵 ↔ {𝐴} ∈ sngl 𝐵)
2 bj-sngltagi 36369 . 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 2098  {csn 4623  sngl bj-csngl 36352  tag bj-ctag 36361
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 2163  ax-ext 2697  ax-sep 5292  ax-pr 5420
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-rex 3065  df-v 3470  df-un 3948  df-in 3950  df-ss 3960  df-sn 4624  df-pr 4626  df-bj-sngl 36353  df-bj-tag 36362
This theorem is referenced by: (None)
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