Theorem inex2 4263

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 3421	. 2 |- ( B i^i A ) = ( A i^i B )
2		inex2.1	. . 3 |- A e. _V
3	2	inex1 4262	. 2 |- ( A i^i B ) e. _V
4	1, 3	eqeltri 2311	1 |- ( B i^i A ) e. _V

Syntax hints:   e. wcel 2209   _Vcvv 2821   i^i cin 3219

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220  ax-sep 4244

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-v 2823  df-in 3226

This theorem is referenced by:  ssex  4265  peano5nnnn  8249  peano5nni  9286  tgdom  15096  distop  15109