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Mirrors > Home > MPE Home > Th. List > suppssdm | Structured version Visualization version Unicode version |
Description: The support of a function is a subset of the function's domain. (Contributed by AV, 30-May-2019.) |
Ref | Expression |
---|---|
suppssdm | supp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | suppval 7297 | . . 3 supp | |
2 | ssrab2 3687 | . . 3 | |
3 | 1, 2 | syl6eqss 3655 | . 2 supp |
4 | supp0prc 7298 | . . 3 supp | |
5 | 0ss 3972 | . . 3 | |
6 | 4, 5 | syl6eqss 3655 | . 2 supp |
7 | 3, 6 | pm2.61i 176 | 1 supp |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wa 384 wcel 1990 wne 2794 crab 2916 cvv 3200 wss 3574 c0 3915 csn 4177 cdm 5114 cima 5117 (class class class)co 6650 supp csupp 7295 |
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-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 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-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-supp 7296 |
This theorem is referenced by: snopsuppss 7310 wemapso2lem 8457 cantnfcl 8564 cantnfle 8568 cantnflt 8569 cantnff 8571 cantnfres 8574 cantnfp1lem2 8576 cantnfp1lem3 8577 cantnflem1b 8583 cantnflem1d 8585 cantnflem1 8586 cantnflem3 8588 cnfcomlem 8596 cnfcom 8597 cnfcom2lem 8598 cnfcom3lem 8600 cnfcom3 8601 fsuppmapnn0fiublem 12789 fsuppmapnn0fiub 12790 fsuppmapnn0fiubOLD 12791 gsumval3lem1 18306 gsumval3lem2 18307 gsumval3 18308 gsumzres 18310 gsumzcl2 18311 gsumzf1o 18313 gsumzaddlem 18321 gsumconst 18334 gsumzoppg 18344 gsum2d 18371 dpjidcl 18457 psrass1lem 19377 psrass1 19405 psrass23l 19408 psrcom 19409 psrass23 19410 mplcoe1 19465 psropprmul 19608 coe1mul2 19639 gsumfsum 19813 regsumsupp 19968 frlmlbs 20136 tsmsgsum 21942 rrxcph 23180 rrxsuppss 23186 rrxmval 23188 mdegfval 23822 mdegleb 23824 mdegldg 23826 deg1mul3le 23876 wilthlem3 24796 fdivmpt 42334 fdivmptf 42335 refdivmptf 42336 fdivpm 42337 refdivpm 42338 |
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