Theorem zfausab 4124

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 3226	. 2 |- { x | ( x e. A /\ ph ) } C_ A
3	1, 2	ssexi 4120	1 |- { x | ( x e. A /\ ph ) } e. _V

Syntax hints:   /\ wa 103   e. wcel 2136   {cab 2151   _Vcvv 2726

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147  ax-sep 4100

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-v 2728  df-in 3122  df-ss 3129

This theorem is referenced by: (None)