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Theorem bj-snglinv 34807
Description: Inverse of singletonization. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
bj-snglinv 𝐴 = {𝑥 ∣ {𝑥} ∈ sngl 𝐴}
Distinct variable group:   𝑥,𝐴

Proof of Theorem bj-snglinv
StepHypRef Expression
1 bj-snglc 34804 . 2 (𝑥𝐴 ↔ {𝑥} ∈ sngl 𝐴)
21abbi2i 2871 1 𝐴 = {𝑥 ∣ {𝑥} ∈ sngl 𝐴}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  wcel 2114  {cab 2716  {csn 4516  sngl bj-csngl 34800
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-11 2162  ax-12 2179  ax-ext 2710  ax-sep 5167  ax-nul 5174  ax-pr 5296
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-tru 1545  df-fal 1555  df-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-rex 3059  df-v 3400  df-dif 3846  df-un 3848  df-nul 4212  df-sn 4517  df-pr 4519  df-bj-sngl 34801
This theorem is referenced by:  bj-snglex  34808  bj-taginv  34821
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