Theorem zfausab 3899

Description: Separation Scheme (Aussonderung) in terms of a class abstraction. (Contributed by NM, 8-Jun-1994.)

Hypothesis

Ref	Expression
zfausab.1	|- A e. _V

Assertion

Ref	Expression
zfausab	|- { x | ( x e. A /\ ph ) } e. _V

Distinct variable group:   x, A

Allowed substitution hint:   ph( x)

Proof of Theorem zfausab

Step	Hyp	Ref	Expression
1		zfausab.1	. 2 |- A e. _V
2		ssab2 3024	. 2 |- { x | ( x e. A /\ ph ) } C_ A
3	1, 2	ssexi 3895	1 |- { x | ( x e. A /\ ph ) } e. _V

Syntax hints:   /\ wa 97   e. wcel 1393   {cab 2026   _Vcvv 2557

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924  df-ss 2931

This theorem is referenced by: (None)