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Theorem ssab2 3188
 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 108 . 2 ((𝑥𝐴𝜑) → 𝑥𝐴)
21abssi 3179 1 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ 𝐴
 Colors of variables: wff set class Syntax hints:   ∧ wa 103   ∈ wcel 2112  {cab 2127   ⊆ wss 3078 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-in 3084  df-ss 3091 This theorem is referenced by:  ssrab2  3189  zfausab  4080  exss  4160  dmopabss  4763  fabexg  5322
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