Theorem zfausab 4186

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 3277	. 2 |- { x | ( x e. A /\ ph ) } C_ A
3	1, 2	ssexi 4182	1 |- { x | ( x e. A /\ ph ) } e. _V

Syntax hints:   /\ wa 104   e. wcel 2176   {cab 2191   _Vcvv 2772

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187  ax-sep 4162

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-in 3172  df-ss 3179

This theorem is referenced by: (None)