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Theorem inex2 3920
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 3157 . 2  |-  ( B  i^i  A )  =  ( A  i^i  B
)
2 inex2.1 . . 3  |-  A  e. 
_V
32inex1 3919 . 2  |-  ( A  i^i  B )  e. 
_V
41, 3eqeltri 2126 1  |-  ( B  i^i  A )  e. 
_V
Colors of variables: wff set class
Syntax hints:    e. wcel 1409   _Vcvv 2574    i^i cin 2944
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-v 2576  df-in 2952
This theorem is referenced by:  ssex  3922  peano5nnnn  7024  peano5nni  7993
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