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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 4776 |
. . . . . . . . 9
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2 | incom 3215 |
. . . . . . . . 9
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3 | 1, 2 | eqtri 2120 |
. . . . . . . 8
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4 | disjsn 3532 |
. . . . . . . . 9
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5 | 4 | biimpri 132 |
. . . . . . . 8
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6 | 3, 5 | syl5eq 2144 |
. . . . . . 7
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7 | 6 | 3ad2ant3 972 |
. . . . . 6
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8 | relres 4783 |
. . . . . . 7
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9 | reldm0 4695 |
. . . . . . 7
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10 | 8, 9 | ax-mp 7 |
. . . . . 6
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11 | 7, 10 | sylibr 133 |
. . . . 5
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12 | fnsng 5106 |
. . . . . . 7
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13 | 12 | 3adant3 969 |
. . . . . 6
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14 | fnresdm 5168 |
. . . . . 6
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15 | 13, 14 | syl 14 |
. . . . 5
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16 | 11, 15 | uneq12d 3178 |
. . . 4
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17 | resundir 4769 |
. . . 4
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18 | uncom 3167 |
. . . . 5
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19 | un0 3343 |
. . . . 5
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20 | 18, 19 | eqtr2i 2121 |
. . . 4
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21 | 16, 17, 20 | 3eqtr4g 2157 |
. . 3
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22 | 21 | fveq1d 5355 |
. 2
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23 | snidg 3501 |
. . . 4
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24 | 23 | 3ad2ant1 970 |
. . 3
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25 | fvres 5377 |
. . 3
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26 | 24, 25 | syl 14 |
. 2
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27 | fvsng 5548 |
. . 3
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28 | 27 | 3adant3 969 |
. 2
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29 | 22, 26, 28 | 3eqtr3d 2140 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-14 1460 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-pow 4038 ax-pr 4069 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-fal 1305 df-nf 1405 df-sb 1704 df-eu 1963 df-mo 1964 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-v 2643 df-sbc 2863 df-dif 3023 df-un 3025 df-in 3027 df-ss 3034 df-nul 3311 df-pw 3459 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-br 3876 df-opab 3930 df-id 4153 df-xp 4483 df-rel 4484 df-cnv 4485 df-co 4486 df-dm 4487 df-res 4489 df-iota 5024 df-fun 5061 df-fn 5062 df-fv 5067 |
This theorem is referenced by: tfrlemisucaccv 6152 tfr1onlemsucaccv 6168 tfrcllemsucaccv 6181 inftonninf 10055 hashinfom 10365 zfz1isolemiso 10423 fvsetsid 11775 |
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