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Mirrors > Home > ILE Home > Th. List > iscn | Unicode version |
Description: The predicate "the class is a continuous function from topology to topology ". Definition of continuous function in [Munkres] p. 102. (Contributed by NM, 17-Oct-2006.) (Revised by Mario Carneiro, 21-Aug-2015.) |
Ref | Expression |
---|---|
iscn | TopOn TopOn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnfval 12363 | . . 3 TopOn TopOn | |
2 | 1 | eleq2d 2209 | . 2 TopOn TopOn |
3 | cnveq 4713 | . . . . . . 7 | |
4 | 3 | imaeq1d 4880 | . . . . . 6 |
5 | 4 | eleq1d 2208 | . . . . 5 |
6 | 5 | ralbidv 2437 | . . . 4 |
7 | 6 | elrab 2840 | . . 3 |
8 | toponmax 12192 | . . . . 5 TopOn | |
9 | toponmax 12192 | . . . . 5 TopOn | |
10 | elmapg 6555 | . . . . 5 | |
11 | 8, 9, 10 | syl2anr 288 | . . . 4 TopOn TopOn |
12 | 11 | anbi1d 460 | . . 3 TopOn TopOn |
13 | 7, 12 | syl5bb 191 | . 2 TopOn TopOn |
14 | 2, 13 | bitrd 187 | 1 TopOn TopOn |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 wral 2416 crab 2420 ccnv 4538 cima 4542 wf 5119 cfv 5123 (class class class)co 5774 cmap 6542 TopOnctopon 12177 ccn 12354 |
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-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 ax-setind 4452 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-ral 2421 df-rex 2422 df-rab 2425 df-v 2688 df-sbc 2910 df-csb 3004 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-iun 3815 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-fv 5131 df-ov 5777 df-oprab 5778 df-mpo 5779 df-1st 6038 df-2nd 6039 df-map 6544 df-top 12165 df-topon 12178 df-cn 12357 |
This theorem is referenced by: iscn2 12369 cnf2 12374 tgcn 12377 ssidcn 12379 cnntr 12394 cnss1 12395 cnss2 12396 cncnp 12399 cnrest 12404 cnrest2 12405 cndis 12410 tx1cn 12438 tx2cn 12439 txdis1cn 12447 |
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