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Theorem bj-snglinv 33452
 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 33449 . 2 (𝑥𝐴 ↔ {𝑥} ∈ sngl 𝐴)
21abbi2i 2915 1 𝐴 = {𝑥 ∣ {𝑥} ∈ sngl 𝐴}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1653   ∈ wcel 2157  {cab 2785  {csn 4368  sngl bj-csngl 33445 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2377  ax-ext 2777  ax-sep 4975  ax-nul 4983  ax-pr 5097 This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2786  df-cleq 2792  df-clel 2795  df-nfc 2930  df-ral 3094  df-rex 3095  df-v 3387  df-dif 3772  df-un 3774  df-nul 4116  df-sn 4369  df-pr 4371  df-bj-sngl 33446 This theorem is referenced by:  bj-snglex  33453  bj-taginv  33466
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