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Theorem zfausab 4771
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 3665 . 2 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ 𝐴
31, 2ssexi 4763 1 {𝑥 ∣ (𝑥𝐴𝜑)} ∈ V
Colors of variables: wff setvar class
Syntax hints:  wa 384  wcel 1987  {cab 2607  Vcvv 3186
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4741
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3188  df-in 3562  df-ss 3569
This theorem is referenced by:  rabfmpunirn  29292
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