Theorem inex2 2713

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 2205	. 2 |- (B i^i A) = (A i^i B)
2		inex2.1	. . 3 |- A e. V
3	2	inex1 2712	. 2 |- (A i^i B) e. V
4	1, 3	eqeltr 1542	1 |- (B i^i A) e. V

Syntax hints:   e. wcel 957  Vcvv 1808   i^i cin 2043

This theorem is referenced by:  ssex 2715  wefrc 2939  abfii2 4545  aceq5lem5 4722  weth 4770  distop 7609  atoml 10265

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1209  ax-11o 1217  ax-ext 1458  ax-sep 2699

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980  df-sb 1171  df-clab 1463  df-cleq 1468  df-clel 1471  df-v 1809  df-in 2048

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