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Mirrors > Home > ILE Home > Th. List > cntop2 | Unicode version |
Description: Reverse closure for a continuous function. (Contributed by Mario Carneiro, 21-Aug-2015.) |
Ref | Expression |
---|---|
cntop2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2170 | . . . 4 | |
2 | eqid 2170 | . . . 4 | |
3 | 1, 2 | iscn2 12994 | . . 3 |
4 | 3 | simplbi 272 | . 2 |
5 | 4 | simprd 113 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 2141 wral 2448 cuni 3796 ccnv 4610 cima 4614 wf 5194 (class class class)co 5853 ctop 12789 ccn 12979 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 ax-un 4418 ax-setind 4521 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ne 2341 df-ral 2453 df-rex 2454 df-rab 2457 df-v 2732 df-sbc 2956 df-csb 3050 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-iun 3875 df-br 3990 df-opab 4051 df-mpt 4052 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-rn 4622 df-res 4623 df-ima 4624 df-iota 5160 df-fun 5200 df-fn 5201 df-f 5202 df-fv 5206 df-ov 5856 df-oprab 5857 df-mpo 5858 df-1st 6119 df-2nd 6120 df-map 6628 df-top 12790 df-topon 12803 df-cn 12982 |
This theorem is referenced by: cnco 13015 cnntri 13018 cnss1 13020 cncnpi 13022 cncnp2m 13025 cnrest 13029 cnrest2r 13031 lmcn 13045 txcnmpt 13067 uptx 13068 lmcn2 13074 cnmpt11 13077 cnmpt11f 13078 cnmpt1t 13079 cnmpt12 13081 cnmpt21 13085 cnmpt2t 13087 cnmpt22 13088 cnmpt22f 13089 cnmptcom 13092 hmeof1o 13103 hmeontr 13107 hmeores 13109 txhmeo 13113 |
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