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Theorem dfv2 3483
Description: Alternate definition of the universal class (see df-v 3482). (Contributed by BJ, 30-Nov-2019.)
Assertion
Ref Expression
dfv2 V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2
StepHypRef Expression
1 df-v 3482 . 2 V = {𝑥𝑥 = 𝑥}
2 equid 2011 . . . 4 𝑥 = 𝑥
32bitru 1549 . . 3 (𝑥 = 𝑥 ↔ ⊤)
43abbii 2809 . 2 {𝑥𝑥 = 𝑥} = {𝑥 ∣ ⊤}
51, 4eqtri 2765 1 V = {𝑥 ∣ ⊤}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  wtru 1541  {cab 2714  Vcvv 3480
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-v 3482
This theorem is referenced by:  vex  3484  abv  3492  vn0  4345  ab0orv  4383  bj-abv  36907
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