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Theorem ssab2 4089
Description: Subclass relation for the restriction of a class abstraction. (Contributed by NM, 31-Mar-1995.)
Assertion
Ref Expression
ssab2 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ 𝐴
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem ssab2
StepHypRef Expression
1 simpl 482 . 2 ((𝑥𝐴𝜑) → 𝑥𝐴)
21abssi 4080 1 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ 𝐴
Colors of variables: wff setvar class
Syntax hints:  wa 395  wcel 2106  {cab 2712  wss 3963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ss 3980
This theorem is referenced by:  zfausab  5338  exss  5474  dmopabss  5932  rnopabss  5969  fabexgOLD  7960  isf32lem9  10399  psubspset  39727  psubclsetN  39919
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