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Theorem zfausab 4142
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
StepHypRef Expression
1 zfausab.1 . 2  |-  A  e. 
_V
2 ssab2 3239 . 2  |-  { x  |  ( x  e.  A  /\  ph ) }  C_  A
31, 2ssexi 4138 1  |-  { x  |  ( x  e.  A  /\  ph ) }  e.  _V
Colors of variables: wff set class
Syntax hints:    /\ wa 104    e. wcel 2148   {cab 2163   _Vcvv 2737
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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-sep 4118
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-in 3135  df-ss 3142
This theorem is referenced by: (None)
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