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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 34427 | . 2 ⊢ WLim(𝑅, 𝐴) = {𝑥 ∈ 𝐴 ∣ (𝑥 ≠ inf(𝐴, 𝐴, 𝑅) ∧ 𝑥 = sup(Pred(𝑅, 𝐴, 𝑥), 𝐴, 𝑅))} | |
2 | 1 | ssrab3 4045 | 1 ⊢ WLim(𝑅, 𝐴) ⊆ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 397 = wceq 1542 ≠ wne 2944 ⊆ wss 3915 Predcpred 6257 supcsup 9383 infcinf 9384 WLimcwlim 34425 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2708 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2715 df-cleq 2729 df-clel 2815 df-rab 3411 df-v 3450 df-in 3922 df-ss 3932 df-wlim 34427 |
This theorem is referenced by: (None) |
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