Theorem dfv2 3481

Description: Alternate definition of the universal class (see df-v 3480). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3480	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2009	. . . 4 ⊢ 𝑥 = 𝑥
3	2	bitru 1546	. . 3 ⊢ (𝑥 = 𝑥 ↔ ⊤)
4	3	abbii 2807	. 2 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑥 ∣ ⊤}
5	1, 4	eqtri 2763	1 ⊢ V = {𝑥 ∣ ⊤}

Syntax hints:   = wceq 1537  ⊤wtru 1538  {cab 2712  Vcvv 3478

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-v 3480

This theorem is referenced by:  vex  3482  abv  3490  vn0  4351  ab0orv  4389  bj-abv  36889