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Mirrors > Home > MPE Home > Th. List > eufnfv | Structured version Visualization version Unicode version |
Description: A function is uniquely determined by its values. (Contributed by NM, 31-Aug-2011.) |
Ref | Expression |
---|---|
eufnfv.1 |
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eufnfv.2 |
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Ref | Expression |
---|---|
eufnfv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eufnfv.1 |
. . . . 5
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2 | 1 | mptex 6152 |
. . . 4
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3 | eqeq2 2482 |
. . . . . 6
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4 | 3 | bibi2d 325 |
. . . . 5
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5 | 4 | albidv 1775 |
. . . 4
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6 | 2, 5 | spcev 3127 |
. . 3
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7 | eufnfv.2 |
. . . . . . 7
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8 | eqid 2471 |
. . . . . . 7
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9 | 7, 8 | fnmpti 5716 |
. . . . . 6
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10 | fneq1 5674 |
. . . . . 6
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11 | 9, 10 | mpbiri 241 |
. . . . 5
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12 | 11 | pm4.71ri 645 |
. . . 4
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13 | dffn5 5924 |
. . . . . . 7
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14 | eqeq1 2475 |
. . . . . . 7
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15 | 13, 14 | sylbi 200 |
. . . . . 6
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16 | fvex 5889 |
. . . . . . . 8
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17 | 16 | rgenw 2768 |
. . . . . . 7
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18 | mpteqb 5979 |
. . . . . . 7
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19 | 17, 18 | ax-mp 5 |
. . . . . 6
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20 | 15, 19 | syl6bb 269 |
. . . . 5
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21 | 20 | pm5.32i 649 |
. . . 4
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22 | 12, 21 | bitr2i 258 |
. . 3
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23 | 6, 22 | mpg 1679 |
. 2
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24 | df-eu 2323 |
. 2
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25 | 23, 24 | mpbir 214 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-8 1906 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-rep 4508 ax-sep 4518 ax-nul 4527 ax-pow 4579 ax-pr 4639 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-mo 2324 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-ral 2761 df-rex 2762 df-reu 2763 df-rab 2765 df-v 3033 df-sbc 3256 df-csb 3350 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-iun 4271 df-br 4396 df-opab 4455 df-mpt 4456 df-id 4754 df-xp 4845 df-rel 4846 df-cnv 4847 df-co 4848 df-dm 4849 df-rn 4850 df-res 4851 df-ima 4852 df-iota 5553 df-fun 5591 df-fn 5592 df-f 5593 df-f1 5594 df-fo 5595 df-f1o 5596 df-fv 5597 |
This theorem is referenced by: (None) |
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