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Mirrors > Home > MPE Home > Th. List > funmpt | Structured version Visualization version Unicode version |
Description: A function in maps-to notation is a function. (Contributed by Mario Carneiro, 13-Jan-2013.) |
Ref | Expression |
---|---|
funmpt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funopab4 5925 | . 2 | |
2 | df-mpt 4730 | . . 3 | |
3 | 2 | funeqi 5909 | . 2 |
4 | 1, 3 | mpbir 221 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wceq 1483 wcel 1990 copab 4712 cmpt 4729 wfun 5882 |
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-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
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-ral 2917 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 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-fun 5890 |
This theorem is referenced by: funmpt2 5927 resfunexg 6479 mptexg 6484 mptexgf 6485 brtpos2 7358 tposfun 7368 mptfi 8265 sniffsupp 8315 cantnfrescl 8573 cantnflem1 8586 r0weon 8835 axcc2lem 9258 mptct 9360 negfi 10971 mptnn0fsupp 12797 ccatalpha 13375 mreacs 16319 acsfn 16320 isofval 16417 lubfun 16980 glbfun 16993 acsficl2d 17176 pmtrsn 17939 gsum2dlem2 18370 gsum2d 18371 dprdfinv 18418 dprdfadd 18419 dmdprdsplitlem 18436 dpjidcl 18457 mptscmfsupp0 18928 00lsp 18981 psrass1lem 19377 psrlidm 19403 psrridm 19404 psrass1 19405 psrass23l 19408 psrcom 19409 psrass23 19410 mplsubrg 19440 mplmon 19463 mplmonmul 19464 mplcoe1 19465 mplcoe5 19468 mplbas2 19470 evlslem2 19512 evlslem6 19513 psropprmul 19608 coe1mul2 19639 pjpm 20052 frlmphllem 20119 frlmphl 20120 uvcff 20130 uvcresum 20132 oftpos 20258 pmatcollpw2lem 20582 tgrest 20963 cmpfi 21211 1stcrestlem 21255 ptcnplem 21424 xkoinjcn 21490 symgtgp 21905 eltsms 21936 rrxmval 23188 tdeglem4 23820 plypf1 23968 tayl0 24116 taylthlem1 24127 xrlimcnp 24695 abrexexd 29347 fmptcof2 29457 ofpreima 29465 funcnvmptOLD 29467 mptctf 29495 psgnfzto1stlem 29850 locfinreflem 29907 measdivcstOLD 30287 sxbrsigalem0 30333 sitgf 30409 nosupno 31849 imageval 32037 poimirlem30 33439 poimir 33442 choicefi 39392 fourierdlem80 40403 sge0tsms 40597 scmsuppss 42153 rmfsupp 42155 scmfsupp 42159 fdivval 42333 |
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