Theorem dfv2 3456

Description: Alternate definition of the universal class (see df-v 3455). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3455	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2031	. . . 4 ⊢ 𝑥 = 𝑥
3	2	bitru 1568	. . 3 ⊢ (𝑥 = 𝑥 ↔ ⊤)
4	3	abbii 2828	. 2 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑥 ∣ ⊤}
5	1, 4	eqtri 2784	1 ⊢ V = {𝑥 ∣ ⊤}

Syntax hints:   = wceq 1559  ⊤wtru 1560  {cab 2739  Vcvv 3453

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1562  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-v 3455

This theorem is referenced by:  vex  3457  abv  3465  vn0  4297  ab0orv  4335  bj-abv  37355