Theorem dfv2 3439

Description: Alternate definition of the universal class (see df-v 3438). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3438	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2013	. . . 4 ⊢ 𝑥 = 𝑥
3	2	bitru 1550	. . 3 ⊢ (𝑥 = 𝑥 ↔ ⊤)
4	3	abbii 2798	. 2 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑥 ∣ ⊤}
5	1, 4	eqtri 2754	1 ⊢ V = {𝑥 ∣ ⊤}

Syntax hints:   = wceq 1541  ⊤wtru 1542  {cab 2709  Vcvv 3436

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 1911  ax-6 1968  ax-7 2009  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-v 3438

This theorem is referenced by:  vex  3440  abv  3448  vn0  4295  ab0orv  4333  bj-abv  36939