Theorem dfv2 3476

Description: Alternate definition of the universal class (see df-v 3475). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3475	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2014	. . . 4 ⊢ 𝑥 = 𝑥
3	2	bitru 1549	. . 3 ⊢ (𝑥 = 𝑥 ↔ ⊤)
4	3	abbii 2801	. 2 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑥 ∣ ⊤}
5	1, 4	eqtri 2759	1 ⊢ V = {𝑥 ∣ ⊤}

Syntax hints:   = wceq 1540  ⊤wtru 1541  {cab 2708  Vcvv 3473

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-9 2115  ax-ext 2702

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-v 3475

This theorem is referenced by:  vex  3477  abv  3484  vn0  4338  ab0orv  4378  bj-abv  36250