Theorem dfv2 3460

Description: Alternate definition of the universal class (see df-v 3459). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3459	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2035	. . . 4 ⊢ 𝑥 = 𝑥
3	2	bitru 1572	. . 3 ⊢ (𝑥 = 𝑥 ↔ ⊤)
4	3	abbii 2832	. 2 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑥 ∣ ⊤}
5	1, 4	eqtri 2788	1 ⊢ V = {𝑥 ∣ ⊤}

Syntax hints:   = wceq 1563  ⊤wtru 1564  {cab 2743  Vcvv 3457

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-9 2155  ax-ext 2737

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1566  df-ex 1803  df-sb 2094  df-clab 2744  df-cleq 2757  df-v 3459

This theorem is referenced by:  vex  3461  abv  3469  vn0  4300  ab0orv  4339  bj-abv  37403