Theorem dfv2 3491

Description: Alternate definition of the universal class (see df-v 3490). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3490	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2011	. . . 4 ⊢ 𝑥 = 𝑥
3	2	bitru 1546	. . 3 ⊢ (𝑥 = 𝑥 ↔ ⊤)
4	3	abbii 2812	. 2 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑥 ∣ ⊤}
5	1, 4	eqtri 2768	1 ⊢ V = {𝑥 ∣ ⊤}

Syntax hints:   = wceq 1537  ⊤wtru 1538  {cab 2717  Vcvv 3488

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-v 3490

This theorem is referenced by:  vex  3492  abv  3500  vn0  4368  ab0orv  4406  bj-abv  36872