Theorem dfv2 3445

Description: Alternate definition of the universal class (see df-v 3444). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3444	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2014	. . . 4 ⊢ 𝑥 = 𝑥
3	2	bitru 1551	. . 3 ⊢ (𝑥 = 𝑥 ↔ ⊤)
4	3	abbii 2804	. 2 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑥 ∣ ⊤}
5	1, 4	eqtri 2760	1 ⊢ V = {𝑥 ∣ ⊤}

Syntax hints:   = wceq 1542  ⊤wtru 1543  {cab 2715  Vcvv 3442

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-v 3444

This theorem is referenced by:  vex  3446  abv  3454  vn0  4299  ab0orv  4337  bj-abv  37148