Theorem vexOLD 3495

Description: Obsolete version of vex 3494 as of 28-Aug-2023. All setvar variables are sets (see isset 3503). Theorem 6.8 of [Quine] p. 43. (Contributed by NM, 26-May-1993.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
vexOLD	⊢ 𝑥 ∈ V

Proof of Theorem vexOLD

Step	Hyp	Ref	Expression
1		equid 2018	. 2 ⊢ 𝑥 = 𝑥
2		df-v 3493	. . 3 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
3	2	abeq2i 2947	. 2 ⊢ (𝑥 ∈ V ↔ 𝑥 = 𝑥)
4	1, 3	mpbir 233	1 ⊢ 𝑥 ∈ V

Syntax hints:   ∈ wcel 2113  Vcvv 3491

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-12 2176  ax-ext 2792

This theorem depends on definitions:  df-bi 209  df-an 399  df-tru 1539  df-ex 1780  df-sb 2069  df-clab 2799  df-cleq 2813  df-clel 2892  df-v 3493

This theorem is referenced by: (None)