Theorem inex2 4153

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 3342	. 2 |- ( B i^i A ) = ( A i^i B )
2		inex2.1	. . 3 |- A e. _V
3	2	inex1 4152	. 2 |- ( A i^i B ) e. _V
4	1, 3	eqeltri 2262	1 |- ( B i^i A ) e. _V

Syntax hints:   e. wcel 2160   _Vcvv 2752   i^i cin 3143

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-sep 4136

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-in 3150

This theorem is referenced by:  ssex  4155  peano5nnnn  7921  peano5nni  8952  tgdom  14032  distop  14045