Theorem bj-abid2 31970

Description: Remove dependency on ax-13 2234 from abid2 2732. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.)

Assertion

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

Distinct variable group:   𝑥,𝐴

Proof of Theorem bj-abid2

Step	Hyp	Ref	Expression
1		biid 250	. . 3 ⊢ (𝑥 ∈ 𝐴 ↔ 𝑥 ∈ 𝐴)
2	1	bj-abbi2i 31964	. 2 ⊢ 𝐴 = {𝑥 ∣ 𝑥 ∈ 𝐴}
3	2	eqcomi 2619	1 ⊢ {𝑥 ∣ 𝑥 ∈ 𝐴} = 𝐴

Syntax hints:   = wceq 1475   ∈ wcel 1977  {cab 2596

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606

This theorem is referenced by: (None)