Theorem vexOLD 3437

Description: Obsolete version of vex 3436 as of 4-Sep-2024. (Contributed by NM, 26-May-1993.) Remove use of ax-12 2171. (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 2015	. . 3 ⊢ 𝑥 = 𝑥
2	1	vexw 2721	. 2 ⊢ 𝑥 ∈ {𝑥 ∣ 𝑥 = 𝑥}
3		df-v 3434	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
4	2, 3	eleqtrri 2838	1 ⊢ 𝑥 ∈ V

Syntax hints:   ∈ wcel 2106  {cab 2715  Vcvv 3432

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434

This theorem is referenced by: (None)