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Mirrors > Home > ILE Home > Th. List > suppssof1 | Unicode version |
Description: Formula building theorem for support restrictions: vector operation with left annihilator. (Contributed by Stefan O'Rear, 9-Mar-2015.) |
Ref | Expression |
---|---|
suppssof1.s |
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suppssof1.o |
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suppssof1.a |
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suppssof1.b |
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suppssof1.d |
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Ref | Expression |
---|---|
suppssof1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | suppssof1.a |
. . . . . 6
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2 | ffn 4989 |
. . . . . 6
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3 | 1, 2 | syl 14 |
. . . . 5
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4 | suppssof1.b |
. . . . . 6
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5 | ffn 4989 |
. . . . . 6
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6 | 4, 5 | syl 14 |
. . . . 5
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7 | suppssof1.d |
. . . . 5
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8 | inidm 3140 |
. . . . 5
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9 | eqidd 2038 |
. . . . 5
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10 | eqidd 2038 |
. . . . 5
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11 | 3, 6, 7, 7, 8, 9, 10 | offval 5661 |
. . . 4
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12 | 11 | cnveqd 4454 |
. . 3
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13 | 12 | imaeq1d 4610 |
. 2
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14 | 1 | feqmptd 5169 |
. . . . . 6
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15 | 14 | cnveqd 4454 |
. . . . 5
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16 | 15 | imaeq1d 4610 |
. . . 4
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17 | suppssof1.s |
. . . 4
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18 | 16, 17 | eqsstr3d 2974 |
. . 3
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19 | suppssof1.o |
. . 3
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20 | funfvex 5135 |
. . . . 5
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21 | 20 | funfni 4942 |
. . . 4
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22 | 3, 21 | sylan 267 |
. . 3
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23 | 4 | ffvelrnda 5245 |
. . 3
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24 | 18, 19, 22, 23 | suppssov1 5651 |
. 2
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25 | 13, 24 | eqsstrd 2973 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-coll 3863 ax-sep 3866 ax-pow 3918 ax-pr 3935 ax-setind 4220 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-fal 1248 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ne 2203 df-ral 2305 df-rex 2306 df-reu 2307 df-rab 2309 df-v 2553 df-sbc 2759 df-csb 2847 df-dif 2914 df-un 2916 df-in 2918 df-ss 2925 df-pw 3353 df-sn 3373 df-pr 3374 df-op 3376 df-uni 3572 df-iun 3650 df-br 3756 df-opab 3810 df-mpt 3811 df-id 4021 df-xp 4294 df-rel 4295 df-cnv 4296 df-co 4297 df-dm 4298 df-rn 4299 df-res 4300 df-ima 4301 df-iota 4810 df-fun 4847 df-fn 4848 df-f 4849 df-f1 4850 df-fo 4851 df-f1o 4852 df-fv 4853 df-ov 5458 df-oprab 5459 df-mpt2 5460 df-of 5654 |
This theorem is referenced by: (None) |
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