Metamath Proof Explorer

Theorem rabexg

Description: Separation Scheme in terms of a restricted class abstraction. (Contributed by NM, 23-Oct-1999)

Ref Expression
Assertion rabexg 
|- ( A e. V -> { x e. A | ph } e. _V )

Proof

Step Hyp Ref Expression
1 ssrab2 
 |-  { x e. A | ph } C_ A
2 ssexg 
 |-  ( ( { x e. A | ph } C_ A /\ A e. V ) -> { x e. A | ph } e. _V )
3 1 2 mpan 
 |-  ( A e. V -> { x e. A | ph } e. _V )