Theorem inex2 4058

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

Step	Hyp	Ref	Expression
1		incom 3263	. 2 |- ( B i^i A ) = ( A i^i B )
2		inex2.1	. . 3 |- A e. _V
3	2	inex1 4057	. 2 |- ( A i^i B ) e. _V
4	1, 3	eqeltri 2210	1 |- ( B i^i A ) e. _V

Syntax hints:   e. wcel 1480   _Vcvv 2681   i^i cin 3065

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 2119  ax-sep 4041

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-in 3072

This theorem is referenced by:  ssex  4060  peano5nnnn  7693  peano5nni  8716  tgdom  12230  distop  12243