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Mirrors > Home > ILE Home > Th. List > iscn2 | 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 Mario Carneiro, 21-Aug-2015.) |
Ref | Expression |
---|---|
iscn.1 | |
iscn.2 |
Ref | Expression |
---|---|
iscn2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-cn 12828 | . . 3 | |
2 | 1 | elmpocl 6036 | . 2 |
3 | iscn.1 | . . . 4 | |
4 | 3 | toptopon 12656 | . . 3 TopOn |
5 | iscn.2 | . . . 4 | |
6 | 5 | toptopon 12656 | . . 3 TopOn |
7 | iscn 12837 | . . 3 TopOn TopOn | |
8 | 4, 6, 7 | syl2anb 289 | . 2 |
9 | 2, 8 | biadanii 603 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1343 wcel 2136 wral 2444 crab 2448 cuni 3789 ccnv 4603 cima 4607 wf 5184 cfv 5188 (class class class)co 5842 cmap 6614 ctop 12635 TopOnctopon 12648 ccn 12825 |
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 604 ax-in2 605 ax-io 699 ax-5 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-13 2138 ax-14 2139 ax-ext 2147 ax-sep 4100 ax-pow 4153 ax-pr 4187 ax-un 4411 ax-setind 4514 |
This theorem depends on definitions: df-bi 116 df-3an 970 df-tru 1346 df-fal 1349 df-nf 1449 df-sb 1751 df-eu 2017 df-mo 2018 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-ne 2337 df-ral 2449 df-rex 2450 df-rab 2453 df-v 2728 df-sbc 2952 df-csb 3046 df-dif 3118 df-un 3120 df-in 3122 df-ss 3129 df-pw 3561 df-sn 3582 df-pr 3583 df-op 3585 df-uni 3790 df-iun 3868 df-br 3983 df-opab 4044 df-mpt 4045 df-id 4271 df-xp 4610 df-rel 4611 df-cnv 4612 df-co 4613 df-dm 4614 df-rn 4615 df-res 4616 df-ima 4617 df-iota 5153 df-fun 5190 df-fn 5191 df-f 5192 df-fv 5196 df-ov 5845 df-oprab 5846 df-mpo 5847 df-1st 6108 df-2nd 6109 df-map 6616 df-top 12636 df-topon 12649 df-cn 12828 |
This theorem is referenced by: cntop1 12841 cntop2 12842 cnf 12844 cnima 12860 cnco 12861 |
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