Metamath Proof Explorer


Theorem rabexf

Description: Separation Scheme in terms of a restricted class abstraction. (Contributed by Glauco Siliprandi, 23-Oct-2021)

Ref Expression
Hypotheses rabexf.1
|- F/_ x A
rabexf.2
|- A e. V
Assertion rabexf
|- { x e. A | ph } e. _V

Proof

Step Hyp Ref Expression
1 rabexf.1
 |-  F/_ x A
2 rabexf.2
 |-  A e. V
3 1 rabexgf
 |-  ( A e. V -> { x e. A | ph } e. _V )
4 2 3 ax-mp
 |-  { x e. A | ph } e. _V