Theorem dfv2 3435

Description: Alternate definition of the universal class (see df-v 3434). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3434	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2015	. . . 4 ⊢ 𝑥 = 𝑥
3	2	bitru 1548	. . 3 ⊢ (𝑥 = 𝑥 ↔ ⊤)
4	3	abbii 2808	. 2 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑥 ∣ ⊤}
5	1, 4	eqtri 2766	1 ⊢ V = {𝑥 ∣ ⊤}

Syntax hints:   = wceq 1539  ⊤wtru 1540  {cab 2715  Vcvv 3432

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-v 3434

This theorem is referenced by:  vex  3436  abv  3443  vn0  4272  ab0orv  4312  bj-abv  35091