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Theorem inex2 3951
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 3181 . 2 (𝐵𝐴) = (𝐴𝐵)
2 inex2.1 . . 3 𝐴 ∈ V
32inex1 3950 . 2 (𝐴𝐵) ∈ V
41, 3eqeltri 2157 1 (𝐵𝐴) ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1436  Vcvv 2615  cin 2987
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067  ax-sep 3934
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617  df-in 2994
This theorem is referenced by:  ssex  3953  peano5nnnn  7374  peano5nni  8363
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