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Theorem inex2 4589
Description: Separation Scheme (Aussonderung) using class notation. (Contributed by NM, 27-Apr-1994.)
Hypothesis
Ref Expression
inex2.1  |-  A  e. 
_V
Assertion
Ref Expression
inex2  |-  ( B  i^i  A )  e. 
_V

Proof of Theorem inex2
StepHypRef Expression
1 incom 3691 . 2  |-  ( B  i^i  A )  =  ( A  i^i  B
)
2 inex2.1 . . 3  |-  A  e. 
_V
32inex1 4588 . 2  |-  ( A  i^i  B )  e. 
_V
41, 3eqeltri 2551 1  |-  ( B  i^i  A )  e. 
_V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1767   _Vcvv 3113    i^i cin 3475
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-in 3483
This theorem is referenced by:  ssex  4591  wefrc  4873  hartogslem1  7967  infxpenlem  8391  dfac5lem5  8508  fin23lem12  8711  fpwwe2lem12  9019  cnso  13841  ressbas  14545  ressress  14552  rescabs  15063  mgpress  16954  pjfval  18532  tgdom  19274  distop  19291  ustfilxp  20478  elovolm  21649  elovolmr  21650  ovolmge0  21651  ovolgelb  21654  ovolunlem1a  21670  ovolunlem1  21671  ovoliunlem1  21676  ovoliunlem2  21677  ovolshftlem2  21684  ovolicc2  21696  ioombl1  21735  dyadmbl  21772  volsup2  21777  vitali  21785  itg1climres  21884  tayl0  22519  atomli  27005  aomclem6  30637  onfrALTlem3  32414
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