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Mirrors > Home > MPE Home > Th. List > Mathboxes > wlimss | Structured version Visualization version GIF version |
Description: The class of limit points is a subclass of the base class. (Contributed by Scott Fenton, 16-Jun-2018.) |
Ref | Expression |
---|---|
wlimss | ⊢ WLim(𝑅, 𝐴) ⊆ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-wlim 35308 | . 2 ⊢ WLim(𝑅, 𝐴) = {𝑥 ∈ 𝐴 ∣ (𝑥 ≠ inf(𝐴, 𝐴, 𝑅) ∧ 𝑥 = sup(Pred(𝑅, 𝐴, 𝑥), 𝐴, 𝑅))} | |
2 | 1 | ssrab3 4073 | 1 ⊢ WLim(𝑅, 𝐴) ⊆ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 395 = wceq 1533 ≠ wne 2932 ⊆ wss 3941 Predcpred 6290 supcsup 9432 infcinf 9433 WLimcwlim 35306 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2695 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2702 df-cleq 2716 df-clel 2802 df-rab 3425 df-v 3468 df-in 3948 df-ss 3958 df-wlim 35308 |
This theorem is referenced by: (None) |
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