Theorem dfv2 3425

Description: Alternate definition of the universal class (see df-v 3424). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3424	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2016	. . . 4 ⊢ 𝑥 = 𝑥
3	2	bitru 1548	. . 3 ⊢ (𝑥 = 𝑥 ↔ ⊤)
4	3	abbii 2809	. 2 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑥 ∣ ⊤}
5	1, 4	eqtri 2766	1 ⊢ V = {𝑥 ∣ ⊤}

Syntax hints:   = wceq 1539  ⊤wtru 1540  {cab 2715  Vcvv 3422

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-v 3424

This theorem is referenced by:  vex  3426  abv  3433  vn0  4269  ab0orv  4309  bj-abv  35018