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Theorem inex2 3966
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 3190 . 2  |-  ( B  i^i  A )  =  ( A  i^i  B
)
2 inex2.1 . . 3  |-  A  e. 
_V
32inex1 3965 . 2  |-  ( A  i^i  B )  e. 
_V
41, 3eqeltri 2160 1  |-  ( B  i^i  A )  e. 
_V
Colors of variables: wff set class
Syntax hints:    e. wcel 1438   _Vcvv 2619    i^i cin 2996
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3949
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-in 3003
This theorem is referenced by:  ssex  3968  peano5nnnn  7406  peano5nni  8397
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