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Theorem rabex2 4450
Description: Separation Scheme in terms of a restricted class abstraction. (Contributed by AV, 16-Jul-2019.)
Hypotheses
Ref Expression
rabex2.1  |-  B  =  { x  e.  A  |  ps }
rabex2.2  |-  A  e.  V
Assertion
Ref Expression
rabex2  |-  B  e. 
_V
Distinct variable group:    x, A
Allowed substitution hints:    ps( x)    B( x)    V( x)

Proof of Theorem rabex2
StepHypRef Expression
1 rabex2.2 . 2  |-  A  e.  V
2 rabex2.1 . . 3  |-  B  =  { x  e.  A  |  ps }
3 id 22 . . 3  |-  ( A  e.  V  ->  A  e.  V )
42, 3rabexd 4449 . 2  |-  ( A  e.  V  ->  B  e.  _V )
51, 4ax-mp 5 1  |-  B  e. 
_V
Colors of variables: wff setvar class
Syntax hints:    = wceq 1369    e. wcel 1756   {crab 2724   _Vcvv 2977
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423  ax-sep 4418
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2573  df-rab 2729  df-v 2979  df-in 3340  df-ss 3347
This theorem is referenced by:  rab2ex  4451  psrlidm  17479  psrass23  17487  mplsubglem  17515  mpllsslem  17516  mplsubrglem  17522  mplmon  17547  mplmonmul  17548  mplcoe1  17549  evlslem2  17602  evlslem3  17605  evlslem1  17606  psrass23l  30829
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