Theorem dfv2 3401

Description: Alternate definition of the universal class (see df-v 3400). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3400	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2022	. . . 4 ⊢ 𝑥 = 𝑥
3	2	bitru 1552	. . 3 ⊢ (𝑥 = 𝑥 ↔ ⊤)
4	3	abbii 2801	. 2 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑥 ∣ ⊤}
5	1, 4	eqtri 2759	1 ⊢ V = {𝑥 ∣ ⊤}

Syntax hints:   = wceq 1543  ⊤wtru 1544  {cab 2714  Vcvv 3398

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2018  ax-9 2122  ax-ext 2708

This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1546  df-ex 1788  df-sb 2073  df-clab 2715  df-cleq 2728  df-v 3400

This theorem is referenced by:  vex  3402  abv  3409  vn0  4239  ab0orv  4279  bj-abv  34778