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Theorem ssab2 3649
 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 472 . 2 ((𝑥𝐴𝜑) → 𝑥𝐴)
21abssi 3640 1 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ 𝐴
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 383   ∈ wcel 1977  {cab 2596   ⊆ wss 3540 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-in 3547  df-ss 3554 This theorem is referenced by:  ssrab2  3650  zfausab  4738  exss  4858  dmopabss  5258  fabexg  7015  isf32lem9  9066  psubspset  34048  psubclsetN  34240
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