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Theorem zfausab 5214
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 4039 . 2 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ 𝐴
31, 2ssexi 5207 1 {𝑥 ∣ (𝑥𝐴𝜑)} ∈ V
Colors of variables: wff setvar class
Syntax hints:  wa 399  wcel 2115  {cab 2802  Vcvv 3479
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5184
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-rab 3141  df-v 3481  df-in 3925  df-ss 3935
This theorem is referenced by:  rabfmpunirn  30395
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