Metamath Proof Explorer


Theorem dfv2

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

Ref Expression
Assertion dfv2 V = { 𝑥 ∣ ⊤ }

Proof

Step Hyp Ref Expression
1 df-v V = { 𝑥𝑥 = 𝑥 }
2 equid 𝑥 = 𝑥
3 2 bitru ( 𝑥 = 𝑥 ↔ ⊤ )
4 3 abbii { 𝑥𝑥 = 𝑥 } = { 𝑥 ∣ ⊤ }
5 1 4 eqtri V = { 𝑥 ∣ ⊤ }