Theorem bj-abid2 32782

Description: Remove dependency on ax-13 2246 from abid2 2745. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-abid2	|- { x | x e. A } = A

Distinct variable group:   x, A

Proof of Theorem bj-abid2

Step	Hyp	Ref	Expression
1		biid 251	. . 3 |- ( x e. A <-> x e. A )
2	1	bj-abbi2i 32776	. 2 |- A = { x | x e. A }
3	2	eqcomi 2631	1 |- { x | x e. A } = A

Syntax hints:   = wceq 1483   e. wcel 1990   {cab 2608

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618

This theorem is referenced by: (None)