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Theorem rabexg 4039
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 3150 . 2  |-  { x  e.  A  |  ph }  C_  A
2 ssexg 4035 . 2  |-  ( ( { x  e.  A  |  ph }  C_  A  /\  A  e.  V
)  ->  { x  e.  A  |  ph }  e.  _V )
31, 2mpan 418 1  |-  ( A  e.  V  ->  { x  e.  A  |  ph }  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1463   {crab 2395   _Vcvv 2658    C_ wss 3039
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-sep 4014
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rab 2400  df-v 2660  df-in 3045  df-ss 3052
This theorem is referenced by:  rabex  4040  exmidsssnc  4094  exse  4226  frind  4242  elfvmptrab1  5481  mpoxopoveq  6103  diffitest  6747  epttop  12165  cldval  12174  neif  12216  neival  12218  cnfval  12269  cnovex  12271  cnpval  12273  hmeofn  12377  hmeofvalg  12378  ispsmet  12398  ismet  12419  isxmet  12420  blvalps  12463  blval  12464  cncfval  12634
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