Theorem dfv2 3457

Description: Alternate definition of the universal class (see df-v 3456). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3456	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2047	. . . 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 ∣ ⊤}

This proof depends on syntax axioms:   = wceq 1570  ⊤wtru 1571  {cab 2741  Vcvv 3454

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-v 3456

This theorem is used by:  vex  3458  abv  3466  vn0  4294  vn0OLD  4295  ab0orv  4335  bj-abv  38009  bj-vn0ALT  38191