Theorem zfausab 4078

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 3186	. 2 |- { x | ( x e. A /\ ph ) } C_ A
3	1, 2	ssexi 4074	1 |- { x | ( x e. A /\ ph ) } e. _V

Syntax hints:   /\ wa 103   e. wcel 1481   {cab 2126   _Vcvv 2689

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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4054

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-in 3082  df-ss 3089

This theorem is referenced by: (None)