Theorem inex2 3453

Description: Separation Scheme (Aussonderung) using class notation.

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 2787	. 2 |- (B i^i A) = (A i^i B)
2		inex2.1	. . 3 |- A e. _V
3	2	inex1 3452	. 2 |- (A i^i B) e. _V
4	1, 3	eqeltri 1967	1 |- (B i^i A) e. _V

Syntax hints:   e. wcel 1300  _Vcvv 2292   i^i cin 2592

This theorem is referenced by:  ssex 3455  wefrc 3652  abfii2 5652  aceq5lem5 5901  weth 5949  distop 8919  atomli 11954  vtarsu 15263

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-9 1307  ax-10 1308  ax-11 1309  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588  ax-ext 1865  ax-sep 3438

This theorem depends on definitions:  df-bi 164  df-or 241  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-v 2294  df-in 2603

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