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Mirrors > Home > ILE Home > Th. List > fvsnun2 | Unicode version |
Description: The value of a function with one of its ordered pairs replaced, at arguments other than the replaced one. See also fvsnun1 5303. (Contributed by NM, 23-Sep-2007.) |
Ref | Expression |
---|---|
fvsnun.1 |
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fvsnun.2 |
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fvsnun.3 |
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Ref | Expression |
---|---|
fvsnun2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvsnun.3 |
. . . . 5
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2 | 1 | reseq1i 4551 |
. . . 4
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3 | resundir 4569 |
. . . 4
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4 | disjdif 3290 |
. . . . . . 7
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5 | fvsnun.1 |
. . . . . . . . 9
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6 | fvsnun.2 |
. . . . . . . . 9
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7 | 5, 6 | fnsn 4896 |
. . . . . . . 8
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8 | fnresdisj 4952 |
. . . . . . . 8
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9 | 7, 8 | ax-mp 7 |
. . . . . . 7
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10 | 4, 9 | mpbi 133 |
. . . . . 6
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11 | residm 4585 |
. . . . . 6
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12 | 10, 11 | uneq12i 3089 |
. . . . 5
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13 | uncom 3081 |
. . . . 5
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14 | un0 3245 |
. . . . 5
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15 | 12, 13, 14 | 3eqtri 2061 |
. . . 4
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16 | 2, 3, 15 | 3eqtri 2061 |
. . 3
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17 | 16 | fveq1i 5122 |
. 2
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18 | fvres 5141 |
. 2
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19 | fvres 5141 |
. 2
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20 | 17, 18, 19 | 3eqtr3a 2093 |
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-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: (None) |
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