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Mirrors > Home > ILE Home > Th. List > fvsnun1 | Unicode version |
Description: The value of a function with one of its ordered pairs replaced, at the replaced ordered pair. See also fvsnun2 5727. (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 |
---|---|
fvsnun1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvsnun.3 |
. . . . 5
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2 | 1 | reseq1i 4915 |
. . . 4
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3 | resundir 4933 |
. . . . 5
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4 | incom 3339 |
. . . . . . . . 9
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5 | disjdif 3507 |
. . . . . . . . 9
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6 | 4, 5 | eqtri 2208 |
. . . . . . . 8
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7 | resdisj 5069 |
. . . . . . . 8
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8 | 6, 7 | ax-mp 5 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | 8 | uneq2i 3298 |
. . . . . 6
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10 | un0 3468 |
. . . . . 6
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11 | 9, 10 | eqtri 2208 |
. . . . 5
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12 | 3, 11 | eqtri 2208 |
. . . 4
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13 | 2, 12 | eqtri 2208 |
. . 3
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14 | 13 | fveq1i 5528 |
. 2
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15 | fvsnun.1 |
. . . 4
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16 | 15 | snid 3635 |
. . 3
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17 | fvres 5551 |
. . 3
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18 | 16, 17 | ax-mp 5 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | fvres 5551 |
. . . 4
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20 | 16, 19 | ax-mp 5 |
. . 3
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21 | fvsnun.2 |
. . . 4
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22 | 15, 21 | fvsn 5724 |
. . 3
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23 | 20, 22 | eqtri 2208 |
. 2
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24 | 14, 18, 23 | 3eqtr3i 2216 |
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 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-v 2751 df-sbc 2975 df-dif 3143 df-un 3145 df-in 3147 df-ss 3154 df-nul 3435 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-br 4016 df-opab 4077 df-id 4305 df-xp 4644 df-rel 4645 df-cnv 4646 df-co 4647 df-dm 4648 df-res 4650 df-iota 5190 df-fun 5230 df-fv 5236 |
This theorem is referenced by: fac0 10722 |
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