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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 4946 |
. . . . . . . . 9
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2 | incom 3342 |
. . . . . . . . 9
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3 | 1, 2 | eqtri 2210 |
. . . . . . . 8
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4 | disjsn 3669 |
. . . . . . . . 9
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5 | 4 | biimpri 133 |
. . . . . . . 8
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6 | 3, 5 | eqtrid 2234 |
. . . . . . 7
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7 | 6 | 3ad2ant3 1022 |
. . . . . 6
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8 | relres 4953 |
. . . . . . 7
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9 | reldm0 4863 |
. . . . . . 7
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10 | 8, 9 | ax-mp 5 |
. . . . . 6
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11 | 7, 10 | sylibr 134 |
. . . . 5
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12 | fnsng 5282 |
. . . . . . 7
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13 | 12 | 3adant3 1019 |
. . . . . 6
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14 | fnresdm 5344 |
. . . . . 6
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15 | 13, 14 | syl 14 |
. . . . 5
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16 | 11, 15 | uneq12d 3305 |
. . . 4
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17 | resundir 4939 |
. . . 4
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18 | uncom 3294 |
. . . . 5
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19 | un0 3471 |
. . . . 5
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20 | 18, 19 | eqtr2i 2211 |
. . . 4
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21 | 16, 17, 20 | 3eqtr4g 2247 |
. . 3
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22 | 21 | fveq1d 5536 |
. 2
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23 | snidg 3636 |
. . . 4
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24 | 23 | 3ad2ant1 1020 |
. . 3
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25 | fvres 5558 |
. . 3
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26 | 24, 25 | syl 14 |
. 2
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27 | fvsng 5733 |
. . 3
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28 | 27 | 3adant3 1019 |
. 2
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29 | 22, 26, 28 | 3eqtr3d 2230 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-sbc 2978 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-nul 3438 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-res 4656 df-iota 5196 df-fun 5237 df-fn 5238 df-fv 5243 |
This theorem is referenced by: tfrlemisucaccv 6350 tfr1onlemsucaccv 6366 tfrcllemsucaccv 6379 inftonninf 10472 hashinfom 10790 zfz1isolemiso 10851 fvsetsid 12546 |
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