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Theorem zfausab 4962
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 3827 . 2 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ 𝐴
31, 2ssexi 4955 1 {𝑥 ∣ (𝑥𝐴𝜑)} ∈ V
Colors of variables: wff setvar class
Syntax hints:  wa 383  wcel 2139  {cab 2746  Vcvv 3340
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740  ax-sep 4933
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-v 3342  df-in 3722  df-ss 3729
This theorem is referenced by:  rabfmpunirn  29783
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