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Mirrors > Home > MPE Home > Th. List > cnf2 | Structured version Visualization version Unicode version |
Description: A continuous function is a mapping. (Contributed by Mario Carneiro, 21-Aug-2015.) |
Ref | Expression |
---|---|
cnf2 | TopOn TopOn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iscn 21039 | . . 3 TopOn TopOn | |
2 | 1 | simprbda 653 | . 2 TopOn TopOn |
3 | 2 | 3impa 1259 | 1 TopOn TopOn |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wcel 1990 wral 2912 ccnv 5113 cima 5117 wf 5884 cfv 5888 (class class class)co 6650 TopOnctopon 20715 ccn 21028 |
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 ax-un 6949 |
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-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-map 7859 df-top 20699 df-topon 20716 df-cn 21031 |
This theorem is referenced by: iscncl 21073 cncls2 21077 cncls 21078 cnntr 21079 cnrest2 21090 cnrest2r 21091 ptcn 21430 txdis1cn 21438 lmcn2 21452 cnmpt11 21466 cnmpt1t 21468 cnmpt12 21470 cnmpt21 21474 cnmpt2t 21476 cnmpt22 21477 cnmpt22f 21478 cnmptcom 21481 cnmptkp 21483 cnmptk1 21484 cnmpt1k 21485 cnmptkk 21486 cnmptk1p 21488 cnmptk2 21489 cnmpt2k 21491 qtopss 21518 qtopeu 21519 qtopomap 21521 qtopcmap 21522 hmeof1o2 21566 xpstopnlem1 21612 xkocnv 21617 xkohmeo 21618 qtophmeo 21620 cnmpt1plusg 21891 cnmpt2plusg 21892 tsmsmhm 21949 cnmpt1vsca 21997 cnmpt2vsca 21998 cnmpt1ds 22645 cnmpt2ds 22646 fsumcn 22673 cnmpt2pc 22727 htpyco1 22777 htpyco2 22778 phtpyco2 22789 pi1xfrf 22853 pi1xfr 22855 pi1xfrcnvlem 22856 pi1xfrcnv 22857 pi1cof 22859 pi1coghm 22861 cnmpt1ip 23046 cnmpt2ip 23047 txsconnlem 31222 txsconn 31223 cvmlift3lem6 31306 fcnre 39184 refsumcn 39189 refsum2cnlem1 39196 fprodcnlem 39831 icccncfext 40100 itgsubsticclem 40191 |
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