ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  inex2 Unicode version

Theorem inex2 4063
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 3268 . 2  |-  ( B  i^i  A )  =  ( A  i^i  B
)
2 inex2.1 . . 3  |-  A  e. 
_V
32inex1 4062 . 2  |-  ( A  i^i  B )  e. 
_V
41, 3eqeltri 2212 1  |-  ( B  i^i  A )  e. 
_V
Colors of variables: wff set class
Syntax hints:    e. wcel 1480   _Vcvv 2686    i^i cin 3070
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-in 3077
This theorem is referenced by:  ssex  4065  peano5nnnn  7707  peano5nni  8730  tgdom  12250  distop  12263
  Copyright terms: Public domain W3C validator