Theorem vexOLD 3402

Description: Obsolete version of vex 3401 as of 4-Sep-2024. (Contributed by NM, 26-May-1993.) Remove use of ax-12 2178. (Revised by SN, 28-Aug-2023.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
vexOLD	⊢ 𝑥 ∈ V

Proof of Theorem vexOLD

Step	Hyp	Ref	Expression
1		equid 2023	. . 3 ⊢ 𝑥 = 𝑥
2	1	vexw 2722	. 2 ⊢ 𝑥 ∈ {𝑥 ∣ 𝑥 = 𝑥}
3		df-v 3399	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
4	2, 3	eleqtrri 2832	1 ⊢ 𝑥 ∈ V

Syntax hints:   ∈ wcel 2113  {cab 2716  Vcvv 3397

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1916  ax-6 1974  ax-7 2019  ax-8 2115  ax-9 2123  ax-ext 2710

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1787  df-sb 2074  df-clab 2717  df-cleq 2730  df-clel 2811  df-v 3399

This theorem is referenced by: (None)