Theorem dfv2 3462

Description: Alternate definition of the universal class (see df-v 3461). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3461	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2011	. . . 4 ⊢ 𝑥 = 𝑥
3	2	bitru 1549	. . 3 ⊢ (𝑥 = 𝑥 ↔ ⊤)
4	3	abbii 2802	. 2 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑥 ∣ ⊤}
5	1, 4	eqtri 2758	1 ⊢ V = {𝑥 ∣ ⊤}

Syntax hints:   = wceq 1540  ⊤wtru 1541  {cab 2713  Vcvv 3459

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-9 2118  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2727  df-v 3461

This theorem is referenced by:  vex  3463  abv  3471  vn0  4320  ab0orv  4358  bj-abv  36924