ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  zfausab Unicode version

Theorem zfausab 4040
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 3151 . 2  |-  { x  |  ( x  e.  A  /\  ph ) }  C_  A
31, 2ssexi 4036 1  |-  { x  |  ( x  e.  A  /\  ph ) }  e.  _V
Colors of variables: wff set class
Syntax hints:    /\ wa 103    e. wcel 1465   {cab 2103   _Vcvv 2660
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-sep 4016
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-in 3047  df-ss 3054
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator