Theorem abid2 2960

Description: A simplification of class abstraction. Commuted form of abid1 2959. See comments there. (Contributed by NM, 26-Dec-1993.)

Assertion

Ref	Expression
abid2	⊢ {𝑥 ∣ 𝑥 ∈ 𝐴} = 𝐴

Distinct variable group:   𝑥,𝐴

Proof of Theorem abid2

Step	Hyp	Ref	Expression
1		abid1 2959	. 2 ⊢ 𝐴 = {𝑥 ∣ 𝑥 ∈ 𝐴}
2	1	eqcomi 2833	1 ⊢ {𝑥 ∣ 𝑥 ∈ 𝐴} = 𝐴

Syntax hints:   = wceq 1536   ∈ wcel 2113  {cab 2802

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 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-ext 2796

This theorem depends on definitions:  df-bi 209  df-an 399  df-tru 1539  df-ex 1780  df-sb 2069  df-clab 2803  df-cleq 2817  df-clel 2896

This theorem is referenced by:  csbid  3899  abss  4043  ssab  4044  abssi  4049  notab  4276  dfrab3  4281  notrab  4283  eusn  4669  uniintsn  4916  iunid  4987  csbexg  5217  imai  5945  dffv4  6670  orduniss2  7551  dfixp  8466  euen1b  8583  modom2  8723  infmap2  9643  cshwsexa  14189  ustfn  22813  ustn0  22832  fpwrelmap  30472  eulerpartlemgvv  31638  ballotlem2  31750  dffv5  33389  ptrest  34895  cnambfre  34944  cnvepresex  35595  pmapglb  36910  polval2N  37046  rngunsnply  39779  iocinico  39824