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Mirrors > Home > ILE Home > Th. List > isnei | Unicode version |
Description: The predicate "the class is a neighborhood of ". (Contributed by FL, 25-Sep-2006.) (Revised by Mario Carneiro, 11-Nov-2013.) |
Ref | Expression |
---|---|
neifval.1 |
Ref | Expression |
---|---|
isnei |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neifval.1 | . . . 4 | |
2 | 1 | neival 12351 | . . 3 |
3 | 2 | eleq2d 2210 | . 2 |
4 | sseq2 3126 | . . . . . . 7 | |
5 | 4 | anbi2d 460 | . . . . . 6 |
6 | 5 | rexbidv 2439 | . . . . 5 |
7 | 6 | elrab 2844 | . . . 4 |
8 | 1 | topopn 12214 | . . . . . 6 |
9 | elpw2g 4089 | . . . . . 6 | |
10 | 8, 9 | syl 14 | . . . . 5 |
11 | 10 | anbi1d 461 | . . . 4 |
12 | 7, 11 | syl5bb 191 | . . 3 |
13 | 12 | adantr 274 | . 2 |
14 | 3, 13 | bitrd 187 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1332 wcel 1481 wrex 2418 crab 2421 wss 3076 cpw 3515 cuni 3744 cfv 5131 ctop 12203 cnei 12346 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-coll 4051 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-reu 2424 df-rab 2426 df-v 2691 df-sbc 2914 df-csb 3008 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-iun 3823 df-br 3938 df-opab 3998 df-mpt 3999 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 df-iota 5096 df-fun 5133 df-fn 5134 df-f 5135 df-f1 5136 df-fo 5137 df-f1o 5138 df-fv 5139 df-top 12204 df-nei 12347 |
This theorem is referenced by: neiint 12353 isneip 12354 neii1 12355 neii2 12357 neiss 12358 neipsm 12362 opnneissb 12363 opnssneib 12364 ssnei2 12365 innei 12371 neitx 12476 |
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