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Theorem rp-abid 43391
Description: Two ways to express a class. (Contributed by RP, 13-Feb-2025.)
Assertion
Ref Expression
rp-abid 𝐴 = {𝑥 ∣ ∃𝑎𝐴 𝑥 = 𝑎}
Distinct variable group:   𝐴,𝑎,𝑥

Proof of Theorem rp-abid
StepHypRef Expression
1 clel5 3665 . 2 (𝑥𝐴 ↔ ∃𝑎𝐴 𝑥 = 𝑎)
21eqabi 2877 1 𝐴 = {𝑥 ∣ ∃𝑎𝐴 𝑥 = 𝑎}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  {cab 2714  wrex 3070
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rex 3071
This theorem is referenced by:  oaun2  43394  oaun3  43395
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