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Theorem ssab2 4074
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 4065 1 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ 𝐴
Colors of variables: wff setvar class
Syntax hints:  wa 395  wcel 2099  {cab 2705  wss 3947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3473  df-in 3954  df-ss 3964
This theorem is referenced by:  ssrab2OLD  4076  zfausab  5332  exss  5465  dmopabss  5921  fabexg  7942  isf32lem9  10385  psubspset  39217  psubclsetN  39409
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