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Mirrors > Home > MPE Home > Th. List > rrxf | Structured version Visualization version Unicode version |
Description: Euclidean vectors as functions. (Contributed by Thierry Arnoux, 7-Jul-2019.) |
Ref | Expression |
---|---|
rrxmval.1 | finSupp |
rrxf.1 |
Ref | Expression |
---|---|
rrxf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rrxmval.1 | . . . 4 finSupp | |
2 | ssrab2 3687 | . . . 4 finSupp | |
3 | 1, 2 | eqsstri 3635 | . . 3 |
4 | rrxf.1 | . . 3 | |
5 | 3, 4 | sseldi 3601 | . 2 |
6 | elmapi 7879 | . 2 | |
7 | 5, 6 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 crab 2916 class class class wbr 4653 wf 5884 (class class class)co 6650 cmap 7857 finSupp cfsupp 8275 cr 9935 cc0 9936 |
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-csb 3534 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-iun 4522 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-1st 7168 df-2nd 7169 df-map 7859 |
This theorem is referenced by: rrxsuppss 23186 rrxmval 23188 rrxmetlem 23190 rrxmet 23191 rrxdstprj1 23192 |
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