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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 33418 | . 2 ⊢ WLim(𝑅, 𝐴) = {𝑥 ∈ 𝐴 ∣ (𝑥 ≠ inf(𝐴, 𝐴, 𝑅) ∧ 𝑥 = sup(Pred(𝑅, 𝐴, 𝑥), 𝐴, 𝑅))} | |
2 | 1 | ssrab3 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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