Metamath Proof Explorer


Theorem bj-vjust

Description: Justification theorem for dfv2 if it were the definition. See also vjust . (Contributed by BJ, 30-Nov-2019) (Proof modification is discouraged.)

Ref Expression
Assertion bj-vjust
|- { x | T. } = { y | T. }

Proof

Step Hyp Ref Expression
1 vextru
 |-  z e. { x | T. }
2 vextru
 |-  z e. { y | T. }
3 1 2 2th
 |-  ( z e. { x | T. } <-> z e. { y | T. } )
4 3 eqriv
 |-  { x | T. } = { y | T. }