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Theorem wlimss 33434
Description: The class of limit points is a subclass of the base class. (Contributed by Scott Fenton, 16-Jun-2018.)
Assertion
Ref Expression
wlimss WLim(𝑅, 𝐴) ⊆ 𝐴

Proof of Theorem wlimss
Dummy variable 𝑥 is distinct from all other variables.
StepHypRef Expression
1 df-wlim 33418 . 2 WLim(𝑅, 𝐴) = {𝑥𝐴 ∣ (𝑥 ≠ inf(𝐴, 𝐴, 𝑅) ∧ 𝑥 = sup(Pred(𝑅, 𝐴, 𝑥), 𝐴, 𝑅))}
21ssrab3 3971 1 WLim(𝑅, 𝐴) ⊆ 𝐴
Colors of variables: wff setvar class
Syntax hints:  wa 399   = wceq 1542  wne 2934  wss 3843  Predcpred 6128  supcsup 8977  infcinf 8978  WLimcwlim 33416
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1545  df-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-rab 3062  df-v 3400  df-in 3850  df-ss 3860  df-wlim 33418
This theorem is referenced by: (None)
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