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Theorem bj-taginv 36522
Description: Inverse of tagging. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
bj-taginv 𝐴 = {𝑥 ∣ {𝑥} ∈ tag 𝐴}
Distinct variable group:   𝑥,𝐴

Proof of Theorem bj-taginv
StepHypRef Expression
1 bj-snglinv 36508 . 2 𝐴 = {𝑥 ∣ {𝑥} ∈ sngl 𝐴}
2 bj-sngltag 36519 . . . 4 (𝑥 ∈ V → ({𝑥} ∈ sngl 𝐴 ↔ {𝑥} ∈ tag 𝐴))
32elv 3469 . . 3 ({𝑥} ∈ sngl 𝐴 ↔ {𝑥} ∈ tag 𝐴)
43abbii 2795 . 2 {𝑥 ∣ {𝑥} ∈ sngl 𝐴} = {𝑥 ∣ {𝑥} ∈ tag 𝐴}
51, 4eqtri 2753 1 𝐴 = {𝑥 ∣ {𝑥} ∈ tag 𝐴}
Colors of variables: wff setvar class
Syntax hints:  wb 205   = wceq 1533  wcel 2098  {cab 2702  Vcvv 3463  {csn 4624  sngl bj-csngl 36501  tag bj-ctag 36510
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 2166  ax-ext 2696  ax-sep 5294  ax-pr 5423
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-rex 3061  df-v 3465  df-dif 3942  df-un 3944  df-ss 3956  df-nul 4319  df-sn 4625  df-pr 4627  df-bj-sngl 36502  df-bj-tag 36511
This theorem is referenced by:  bj-projval  36532
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