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Theorem inex2 3892
 Description: Separation Scheme (Aussonderung) using class notation. (Contributed by NM, 27-Apr-1994.)
Hypothesis
Ref Expression
inex2.1 𝐴 ∈ V
Assertion
Ref Expression
inex2 (𝐵𝐴) ∈ V

Proof of Theorem inex2
StepHypRef Expression
1 incom 3129 . 2 (𝐵𝐴) = (𝐴𝐵)
2 inex2.1 . . 3 𝐴 ∈ V
32inex1 3891 . 2 (𝐴𝐵) ∈ V
41, 3eqeltri 2110 1 (𝐵𝐴) ∈ V
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1393  Vcvv 2557   ∩ cin 2916 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924 This theorem is referenced by:  ssex  3894  peano5nnnn  6966  peano5nni  7917
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