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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 35814 | . 2 ⊢ WLim(𝑅, 𝐴) = {𝑥 ∈ 𝐴 ∣ (𝑥 ≠ inf(𝐴, 𝐴, 𝑅) ∧ 𝑥 = sup(Pred(𝑅, 𝐴, 𝑥), 𝐴, 𝑅))} | |
| 2 | 1 | ssrab3 4082 | 1 ⊢ WLim(𝑅, 𝐴) ⊆ 𝐴 | 
| Colors of variables: wff setvar class | 
| Syntax hints: ∧ wa 395 = wceq 1540 ≠ wne 2940 ⊆ wss 3951 Predcpred 6320 supcsup 9480 infcinf 9481 WLimcwlim 35812 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-rab 3437 df-ss 3968 df-wlim 35814 | 
| This theorem is referenced by: (None) | 
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