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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 32627 | . 2 ⊢ WLim(𝑅, 𝐴) = {𝑥 ∈ 𝐴 ∣ (𝑥 ≠ inf(𝐴, 𝐴, 𝑅) ∧ 𝑥 = sup(Pred(𝑅, 𝐴, 𝑥), 𝐴, 𝑅))} | |
2 | 1 | ssrab3 3947 | 1 ⊢ WLim(𝑅, 𝐴) ⊆ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 387 = wceq 1507 ≠ wne 2967 ⊆ wss 3829 Predcpred 5985 supcsup 8699 infcinf 8700 WLimcwlim 32625 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1758 ax-4 1772 ax-5 1869 ax-6 1928 ax-7 1965 ax-8 2052 ax-9 2059 ax-10 2079 ax-11 2093 ax-12 2106 ax-ext 2750 |
This theorem depends on definitions: df-bi 199 df-an 388 df-or 834 df-tru 1510 df-ex 1743 df-nf 1747 df-sb 2016 df-clab 2759 df-cleq 2771 df-clel 2846 df-nfc 2918 df-rab 3097 df-in 3836 df-ss 3843 df-wlim 32627 |
This theorem is referenced by: (None) |
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