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Theorem bj-taginv 36374
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 36360 . 2 𝐴 = {𝑥 ∣ {𝑥} ∈ sngl 𝐴}
2 bj-sngltag 36371 . . . 4 (𝑥 ∈ V → ({𝑥} ∈ sngl 𝐴 ↔ {𝑥} ∈ tag 𝐴))
32elv 3474 . . 3 ({𝑥} ∈ sngl 𝐴 ↔ {𝑥} ∈ tag 𝐴)
43abbii 2796 . 2 {𝑥 ∣ {𝑥} ∈ sngl 𝐴} = {𝑥 ∣ {𝑥} ∈ tag 𝐴}
51, 4eqtri 2754 1 𝐴 = {𝑥 ∣ {𝑥} ∈ tag 𝐴}
Colors of variables: wff setvar class
Syntax hints:  wb 205   = wceq 1533  wcel 2098  {cab 2703  Vcvv 3468  {csn 4623  sngl bj-csngl 36353  tag bj-ctag 36362
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-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-rex 3065  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-sn 4624  df-pr 4626  df-bj-sngl 36354  df-bj-tag 36363
This theorem is referenced by:  bj-projval  36384
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