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Mirrors > Home > ILE Home > Th. List > fsnunfv | Unicode version |
Description: Recover the added point from a point-added function. (Contributed by Stefan O'Rear, 28-Feb-2015.) (Revised by NM, 18-May-2017.) |
Ref | Expression |
---|---|
fsnunfv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmres 4575 |
. . . . . . . . 9
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2 | incom 3123 |
. . . . . . . . 9
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3 | 1, 2 | eqtri 2057 |
. . . . . . . 8
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4 | disjsn 3423 |
. . . . . . . . 9
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5 | 4 | biimpri 124 |
. . . . . . . 8
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6 | 3, 5 | syl5eq 2081 |
. . . . . . 7
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7 | 6 | 3ad2ant3 926 |
. . . . . 6
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8 | relres 4582 |
. . . . . . 7
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9 | reldm0 4496 |
. . . . . . 7
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10 | 8, 9 | ax-mp 7 |
. . . . . 6
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11 | 7, 10 | sylibr 137 |
. . . . 5
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12 | fnsng 4890 |
. . . . . . 7
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13 | 12 | 3adant3 923 |
. . . . . 6
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14 | fnresdm 4951 |
. . . . . 6
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15 | 13, 14 | syl 14 |
. . . . 5
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16 | 11, 15 | uneq12d 3092 |
. . . 4
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17 | resundir 4569 |
. . . 4
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18 | uncom 3081 |
. . . . 5
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19 | un0 3245 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
20 | 18, 19 | eqtr2i 2058 |
. . . 4
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21 | 16, 17, 20 | 3eqtr4g 2094 |
. . 3
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22 | 21 | fveq1d 5123 |
. 2
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23 | snidg 3392 |
. . . 4
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24 | 23 | 3ad2ant1 924 |
. . 3
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25 | fvres 5141 |
. . 3
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26 | 24, 25 | syl 14 |
. 2
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27 | fvsng 5302 |
. . 3
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28 | 27 | 3adant3 923 |
. 2
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29 | 22, 26, 28 | 3eqtr3d 2077 |
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-sep 3866 ax-pow 3918 ax-pr 3935 |
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-ral 2305 df-rex 2306 df-v 2553 df-sbc 2759 df-dif 2914 df-un 2916 df-in 2918 df-ss 2925 df-nul 3219 df-pw 3353 df-sn 3373 df-pr 3374 df-op 3376 df-uni 3572 df-br 3756 df-opab 3810 df-id 4021 df-xp 4294 df-rel 4295 df-cnv 4296 df-co 4297 df-dm 4298 df-res 4300 df-iota 4810 df-fun 4847 df-fn 4848 df-fv 4853 |
This theorem is referenced by: tfrlemisucaccv 5880 |
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