Theorem rabexf 39319

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

Hypotheses

Ref	Expression
rabexf.1	|- F/_ x A
rabexf.2	|- A e. V

Assertion

Ref	Expression
rabexf	|- { x e. A | ph } e. _V

Proof of Theorem rabexf

Step	Hyp	Ref	Expression
1		rabexf.2	. 2 |- A e. V
2		rabexf.1	. . 3 |- F/_ x A
3	2	rabexgf 39183	. 2 |- ( A e. V -> { x e. A | ph } e. _V )
4	1, 3	ax-mp 5	1 |- { x e. A | ph } e. _V

Syntax hints:   e. wcel 1990   F/_wnfc 2751   {crab 2916   _Vcvv 3200

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-sep 4781

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rab 2921  df-v 3202  df-in 3581  df-ss 3588

This theorem is referenced by:  limsupequzmpt2  39950  liminfequzmpt2  40023