Metamath Proof Explorer


Theorem rabex2

Description: Separation Scheme in terms of a restricted class abstraction. (Contributed by AV, 16-Jul-2019) (Revised by AV, 26-Mar-2021)

Ref Expression
Hypotheses rabex2.1
|- B = { x e. A | ps }
rabex2.2
|- A e. _V
Assertion rabex2
|- B e. _V

Proof

Step Hyp Ref Expression
1 rabex2.1
 |-  B = { x e. A | ps }
2 rabex2.2
 |-  A e. _V
3 id
 |-  ( A e. _V -> A e. _V )
4 1 3 rabexd
 |-  ( A e. _V -> B e. _V )
5 2 4 ax-mp
 |-  B e. _V