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Theorem rabexg 4143
Description: Separation Scheme in terms of a restricted class abstraction. (Contributed by NM, 23-Oct-1999.)
Assertion
Ref Expression
rabexg  |-  ( A  e.  V  ->  { x  e.  A  |  ph }  e.  _V )
Distinct variable group:    x, A
Allowed substitution hints:    ph( x)    V( x)

Proof of Theorem rabexg
StepHypRef Expression
1 ssrab2 3240 . 2  |-  { x  e.  A  |  ph }  C_  A
2 ssexg 4139 . 2  |-  ( ( { x  e.  A  |  ph }  C_  A  /\  A  e.  V
)  ->  { x  e.  A  |  ph }  e.  _V )
31, 2mpan 424 1  |-  ( A  e.  V  ->  { x  e.  A  |  ph }  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2148   {crab 2459   _Vcvv 2737    C_ wss 3129
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-rab 2464  df-v 2739  df-in 3135  df-ss 3142
This theorem is referenced by:  rabex  4144  exmidsssnc  4200  exse  4332  frind  4348  elfvmptrab1  5605  mpoxopoveq  6234  diffitest  6880  supex2g  7025  cc4f  7246  omctfn  12414  ismhm  12730  issubm  12740  epttop  13223  cldval  13232  neif  13274  neival  13276  cnfval  13327  cnovex  13329  cnpval  13331  hmeofn  13435  hmeofvalg  13436  ispsmet  13456  ismet  13477  isxmet  13478  blvalps  13521  blval  13522  cncfval  13692
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