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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 35409 | . 2 ⊢ WLim(𝑅, 𝐴) = {𝑥 ∈ 𝐴 ∣ (𝑥 ≠ inf(𝐴, 𝐴, 𝑅) ∧ 𝑥 = sup(Pred(𝑅, 𝐴, 𝑥), 𝐴, 𝑅))} | |
2 | 1 | ssrab3 4078 | 1 ⊢ WLim(𝑅, 𝐴) ⊆ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 395 = wceq 1534 ≠ wne 2937 ⊆ wss 3947 Predcpred 6304 supcsup 9464 infcinf 9465 WLimcwlim 35407 |
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-rab 3430 df-v 3473 df-in 3954 df-ss 3964 df-wlim 35409 |
This theorem is referenced by: (None) |
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