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Theorem zfausab 4070
 Description: Separation Scheme (Aussonderung) in terms of a class abstraction. (Contributed by NM, 8-Jun-1994.)
Hypothesis
Ref Expression
zfausab.1 𝐴 ∈ V
Assertion
Ref Expression
zfausab {𝑥 ∣ (𝑥𝐴𝜑)} ∈ V
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem zfausab
StepHypRef Expression
1 zfausab.1 . 2 𝐴 ∈ V
2 ssab2 3181 . 2 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ 𝐴
31, 2ssexi 4066 1 {𝑥 ∣ (𝑥𝐴𝜑)} ∈ V
 Colors of variables: wff set class Syntax hints:   ∧ wa 103   ∈ wcel 1480  {cab 2125  Vcvv 2686 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-in 3077  df-ss 3084 This theorem is referenced by: (None)
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