Theorem dfv2 3435

Description: Alternate definition of the universal class (see df-v 3434). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3434	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2019	. . . 4 ⊢ 𝑥 = 𝑥
3	2	bitru 1556	. . 3 ⊢ (𝑥 = 𝑥 ↔ ⊤)
4	3	abbii 2807	. 2 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑥 ∣ ⊤}
5	1, 4	eqtri 2763	1 ⊢ V = {𝑥 ∣ ⊤}

Syntax hints:   = wceq 1547  ⊤wtru 1548  {cab 2718  Vcvv 3432

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-9 2129  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-v 3434

This theorem is referenced by:  vex  3436  abv  3444  vn0  4280  ab0orv  4318  bj-abv  37266