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Theorem islp2 17214
 Description: The predicate " is a limit point of ," in terms of neighborhoods. Definition of limit point in [Munkres] p. 97. Although Munkres uses open neighborhoods, it also works for our more general neighborhoods. (Contributed by NM, 26-Feb-2007.) (Proof shortened by Mario Carneiro, 25-Dec-2016.)
Hypothesis
Ref Expression
lpfval.1
Assertion
Ref Expression
islp2
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem islp2
StepHypRef Expression
1 lpfval.1 . . . 4
21islp 17209 . . 3
4 ssdifss 3480 . . 3
51neindisj2 17192 . . 3
64, 5syl3an2 1219 . 2
73, 6bitrd 246 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   w3a 937   wceq 1653   wcel 1726   wne 2601  wral 2707   cdif 3319   cin 3321   wss 3322  c0 3630  csn 3816  cuni 4017  cfv 5457  ctop 16963  ccl 17087  cnei 17166  clp 17203 This theorem is referenced by:  clslp  17217  lpbl  18538  reperflem  18854 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-rep 4323  ax-sep 4333  ax-nul 4341  ax-pow 4380  ax-pr 4406  ax-un 4704 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-reu 2714  df-rab 2716  df-v 2960  df-sbc 3164  df-csb 3254  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-int 4053  df-iun 4097  df-iin 4098  df-br 4216  df-opab 4270  df-mpt 4271  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-res 4893  df-ima 4894  df-iota 5421  df-fun 5459  df-fn 5460  df-f 5461  df-f1 5462  df-fo 5463  df-f1o 5464  df-fv 5465  df-top 16968  df-cld 17088  df-ntr 17089  df-cls 17090  df-nei 17167  df-lp 17205
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