Theorem inex2 4071

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 3273	. 2 |- ( B i^i A ) = ( A i^i B )
2		inex2.1	. . 3 |- A e. _V
3	2	inex1 4070	. 2 |- ( A i^i B ) e. _V
4	1, 3	eqeltri 2213	1 |- ( B i^i A ) e. _V

Syntax hints:   e. wcel 1481   _Vcvv 2689   i^i cin 3075

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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4054

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-in 3082

This theorem is referenced by:  ssex  4073  peano5nnnn  7724  peano5nni  8747  tgdom  12280  distop  12293