Theorem dfv2 3453

Description: Alternate definition of the universal class (see df-v 3452). (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
dfv2	⊢ V = {𝑥 ∣ ⊤}

Proof of Theorem dfv2

Step	Hyp	Ref	Expression
1		df-v 3452	. 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥}
2		equid 2044	. . . 4 ⊢ 𝑥 = 𝑥
3	2	bitru 1578	. . 3 ⊢ (𝑥 = 𝑥 ↔ ⊤)
4	3	abbii 2827	. 2 ⊢ {𝑥 ∣ 𝑥 = 𝑥} = {𝑥 ∣ ⊤}
5	1, 4	eqtri 2783	1 ⊢ V = {𝑥 ∣ ⊤}

This proof depends on syntax axioms:   = wceq 1569  ⊤wtru 1570  {cab 2738  Vcvv 3450

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-v 3452

This theorem is used by:  vex  3454  abv  3462  vn0  4290  vn0OLD  4291  ab0orv  4331  bj-abv  37911  bj-vn0ALT  38080