Theorem dfv2 3458

Description: Alternate definition of the universal class (see df-v 3457). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3457	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2042	. . . 4 ⊢ 𝑥 = 𝑥
3	2	bitru 1579	. . 3 ⊢ (𝑥 = 𝑥 ↔ ⊤)
4	3	abbii 2830	. 2 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑥 ∣ ⊤}
5	1, 4	eqtri 2786	1 ⊢ V = {𝑥 ∣ ⊤}

Syntax hints:   = wceq 1570  ⊤wtru 1571  {cab 2741  Vcvv 3455

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-v 3457

This theorem is referenced by:  vex  3459  abv  3467  vn0  4299  vn0OLD  4300  ab0orv  4340  bj-abv  37519  bj-vn0ALT  37686