Theorem inex2 1698

Description: Separation Scheme (Aussonderung) using class notation.

Hypothesis

Ref	Expression
inex2.1	⊢ A ∈ V

Assertion

Ref	Expression
inex2	⊢ (B ∩ A) ∈ V

Proof of Theorem inex2

Step	Hyp	Ref	Expression
1		incom 1636	. 2 ⊢ (B ∩ A) = (A ∩ B)
2		inex2.1	. . 3 ⊢ A ∈ V
3	2	inex1 1697	. 2 ⊢ (A ∩ B) ∈ V
4	1, 3	eqeltr 1159	1 ⊢ (B ∩ A) ∈ V

Syntax hints:   ∈ wcel 1092  Vcvv 1348   ∩ cin 1486

This theorem is referenced by:  ssex 1700  wefrc 2195  aceq5lem5 3562  weth 3602

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-14 805  ax-16 922  ax-17 925  ax-ext 1074  ax-rep 1075

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-in 1491

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