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Theorem inex2 4021
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 3232 . 2 (𝐵𝐴) = (𝐴𝐵)
2 inex2.1 . . 3 𝐴 ∈ V
32inex1 4020 . 2 (𝐴𝐵) ∈ V
41, 3eqeltri 2185 1 (𝐵𝐴) ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1461  Vcvv 2655  cin 3034
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095  ax-sep 4004
This theorem depends on definitions:  df-bi 116  df-tru 1315  df-nf 1418  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-nfc 2242  df-v 2657  df-in 3041
This theorem is referenced by:  ssex  4023  peano5nnnn  7621  peano5nni  8627  tgdom  12078  distop  12091
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