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| Description: The topological space convergence relation is a relation. (Contributed by NM, 7-Dec-2006.) (Revised by Mario Carneiro, 14-Nov-2013.) | 
| Ref | Expression | 
|---|---|
| lmrel | ⊢ Rel (⇝𝑡‘𝐽) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | df-lm 23238 | . 2 ⊢ ⇝𝑡 = (𝑗 ∈ Top ↦ {〈𝑓, 𝑥〉 ∣ (𝑓 ∈ (∪ 𝑗 ↑pm ℂ) ∧ 𝑥 ∈ ∪ 𝑗 ∧ ∀𝑢 ∈ 𝑗 (𝑥 ∈ 𝑢 → ∃𝑦 ∈ ran ℤ≥(𝑓 ↾ 𝑦):𝑦⟶𝑢))}) | |
| 2 | 1 | relmptopab 7684 | 1 ⊢ Rel (⇝𝑡‘𝐽) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∧ w3a 1086 ∈ wcel 2107 ∀wral 3060 ∃wrex 3069 ∪ cuni 4906 ran crn 5685 ↾ cres 5686 Rel wrel 5689 ⟶wf 6556 ‘cfv 6560 (class class class)co 7432 ↑pm cpm 8868 ℂcc 11154 ℤ≥cuz 12879 Topctop 22900 ⇝𝑡clm 23235 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-10 2140 ax-11 2156 ax-12 2176 ax-ext 2707 ax-sep 5295 ax-nul 5305 ax-pr 5431 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1542 df-fal 1552 df-ex 1779 df-nf 1783 df-sb 2064 df-mo 2539 df-eu 2568 df-clab 2714 df-cleq 2728 df-clel 2815 df-nfc 2891 df-ral 3061 df-rex 3070 df-rab 3436 df-v 3481 df-sbc 3788 df-csb 3899 df-dif 3953 df-un 3955 df-in 3957 df-ss 3967 df-nul 4333 df-if 4525 df-sn 4626 df-pr 4628 df-op 4632 df-uni 4907 df-br 5143 df-opab 5205 df-mpt 5225 df-id 5577 df-xp 5690 df-rel 5691 df-cnv 5692 df-co 5693 df-dm 5694 df-rn 5695 df-res 5696 df-ima 5697 df-iota 6513 df-fun 6562 df-fv 6568 df-lm 23238 | 
| This theorem is referenced by: lmfun 23390 cmetcaulem 25323 lmle 25336 heibor1lem 37817 rrncmslem 37840 xlimrel 45840 | 
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