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Theorem ssab2 3976
 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 483 . 2 ((𝑥𝐴𝜑) → 𝑥𝐴)
21abssi 3967 1 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ 𝐴
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 396   ∈ wcel 2081  {cab 2775   ⊆ wss 3859 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-8 2083  ax-9 2091  ax-10 2112  ax-11 2126  ax-12 2141  ax-ext 2769 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-tru 1525  df-ex 1762  df-nf 1766  df-sb 2043  df-clab 2776  df-cleq 2788  df-clel 2863  df-nfc 2935  df-in 3866  df-ss 3874 This theorem is referenced by:  ssrab2  3977  zfausab  5124  exss  5247  dmopabss  5673  fabexg  7495  isf32lem9  9629  psubspset  36411  psubclsetN  36603
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