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Mirrors > Home > MPE Home > Th. List > elflim2 | Structured version Visualization version Unicode version |
Description: The predicate "is a limit point of a filter." (Contributed by Mario Carneiro, 9-Apr-2015.) (Revised by Stefan O'Rear, 6-Aug-2015.) |
Ref | Expression |
---|---|
flimval.1 |
Ref | Expression |
---|---|
elflim2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anass 681 | . 2 | |
2 | df-3an 1039 | . . 3 | |
3 | 2 | anbi1i 731 | . 2 |
4 | df-flim 21743 | . . . 4 | |
5 | 4 | elmpt2cl 6876 | . . 3 |
6 | flimval.1 | . . . . . 6 | |
7 | 6 | flimval 21767 | . . . . 5 |
8 | 7 | eleq2d 2687 | . . . 4 |
9 | sneq 4187 | . . . . . . . . . 10 | |
10 | 9 | fveq2d 6195 | . . . . . . . . 9 |
11 | 10 | sseq1d 3632 | . . . . . . . 8 |
12 | 11 | anbi1d 741 | . . . . . . 7 |
13 | ancom 466 | . . . . . . 7 | |
14 | 12, 13 | syl6bb 276 | . . . . . 6 |
15 | 14 | elrab 3363 | . . . . 5 |
16 | an12 838 | . . . . 5 | |
17 | 15, 16 | bitri 264 | . . . 4 |
18 | 8, 17 | syl6bb 276 | . . 3 |
19 | 5, 18 | biadan2 674 | . 2 |
20 | 1, 3, 19 | 3bitr4ri 293 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 crab 2916 wss 3574 cpw 4158 csn 4177 cuni 4436 crn 5115 cfv 5888 (class class class)co 6650 ctop 20698 cnei 20901 cfil 21649 cflim 21738 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-top 20699 df-flim 21743 |
This theorem is referenced by: flimtop 21769 flimneiss 21770 flimelbas 21772 flimfil 21773 elflim 21775 |
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