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Theorem rabexg 3928
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 3053 . 2  |-  { x  e.  A  |  ph }  C_  A
2 ssexg 3924 . 2  |-  ( ( { x  e.  A  |  ph }  C_  A  /\  A  e.  V
)  ->  { x  e.  A  |  ph }  e.  _V )
31, 2mpan 408 1  |-  ( A  e.  V  ->  { x  e.  A  |  ph }  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1409   {crab 2327   _Vcvv 2574    C_ wss 2945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rab 2332  df-v 2576  df-in 2952  df-ss 2959
This theorem is referenced by:  rabex  3929  exse  4101  frind  4117  mpt2xopoveq  5886  diffitest  6375
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