Theorem inex2 2707

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 2198	. 2 |- (B i^i A) = (A i^i B)
2		inex2.1	. . 3 |- A e. V
3	2	inex1 2706	. 2 |- (A i^i B) e. V
4	1, 3	eqeltr 1536	1 |- (B i^i A) e. V

Syntax hints:   e. wcel 955  Vcvv 1802   i^i cin 2036

This theorem is referenced by:  ssex 2709  wefrc 2933  abfii2 4536  aceq5lem5 4711  weth 4759  distop 7591  atoml 10217

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452  ax-sep 2693

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-v 1803  df-in 2041

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