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Metamath Proof Explorer

Theorem inex2

Description: Separation Scheme (Aussonderung) using class notation. (Contributed by NM, 27-Apr-1994)

Ref Expression
Hypothesis inex2.1 ⊢ 𝐴 ∈ V
Assertion inex2 ( 𝐵 ∩ 𝐴 ) ∈ V

Proof

Step Hyp Ref Expression
1 inex2.1 ⊢ 𝐴 ∈ V
2 incom ⊢ ( 𝐵 ∩ 𝐴 ) = ( 𝐴 ∩ 𝐵 )
3 1 inex1 ⊢ ( 𝐴 ∩ 𝐵 ) ∈ V
4 2 3 eqeltri ⊢ ( 𝐵 ∩ 𝐴 ) ∈ V