Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-tagcg Structured version   Visualization version   GIF version

Theorem bj-tagcg 34194
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 34178 . 2 (𝐴𝐵 ↔ {𝐴} ∈ sngl 𝐵)
2 bj-sngltag 34192 . 2 (𝐴𝑉 → ({𝐴} ∈ sngl 𝐵 ↔ {𝐴} ∈ tag 𝐵))
31, 2syl5bb 284 1 (𝐴𝑉 → (𝐴𝐵 ↔ {𝐴} ∈ tag 𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  wcel 2105  {csn 4557  sngl bj-csngl 34174  tag bj-ctag 34183
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790  ax-sep 5194  ax-nul 5201  ax-pr 5320
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-rex 3141  df-v 3494  df-dif 3936  df-un 3938  df-in 3940  df-ss 3949  df-nul 4289  df-sn 4558  df-pr 4560  df-bj-sngl 34175  df-bj-tag 34184
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator