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Theorem ssab2 3894
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 470 . 2 ((𝑥𝐴𝜑) → 𝑥𝐴)
21abssi 3885 1 {𝑥 ∣ (𝑥𝐴𝜑)} ⊆ 𝐴
Colors of variables: wff setvar class
Syntax hints:  wa 384  wcel 2157  {cab 2803  wss 3780
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2069  ax-7 2105  ax-9 2166  ax-10 2186  ax-11 2202  ax-12 2215  ax-13 2422  ax-ext 2795
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-tru 1641  df-ex 1860  df-nf 1864  df-sb 2062  df-clab 2804  df-cleq 2810  df-clel 2813  df-nfc 2948  df-in 3787  df-ss 3794
This theorem is referenced by:  ssrab2  3895  zfausab  5016  exss  5132  dmopabss  5548  fabexg  7359  isf32lem9  9475  psubspset  35530  psubclsetN  35722
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