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Mirrors > Home > ILE Home > Th. List > funtp | Unicode version |
Description: A function with a domain of three elements. (Contributed by NM, 14-Sep-2011.) |
Ref | Expression |
---|---|
funtp.1 |
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funtp.2 |
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funtp.3 |
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funtp.4 |
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funtp.5 |
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funtp.6 |
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Ref | Expression |
---|---|
funtp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funtp.1 |
. . . . . 6
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2 | funtp.2 |
. . . . . 6
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3 | funtp.4 |
. . . . . 6
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4 | funtp.5 |
. . . . . 6
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5 | 1, 2, 3, 4 | funpr 5263 |
. . . . 5
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6 | funtp.3 |
. . . . . 6
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7 | funtp.6 |
. . . . . 6
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8 | 6, 7 | funsn 5259 |
. . . . 5
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9 | 5, 8 | jctir 313 |
. . . 4
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10 | 3, 4 | dmprop 5098 |
. . . . . . 7
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11 | df-pr 3598 |
. . . . . . 7
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12 | 10, 11 | eqtri 2198 |
. . . . . 6
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13 | 7 | dmsnop 5097 |
. . . . . 6
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14 | 12, 13 | ineq12i 3334 |
. . . . 5
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15 | disjsn2 3654 |
. . . . . . 7
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16 | disjsn2 3654 |
. . . . . . 7
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17 | 15, 16 | anim12i 338 |
. . . . . 6
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18 | undisj1 3480 |
. . . . . 6
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19 | 17, 18 | sylib 122 |
. . . . 5
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20 | 14, 19 | eqtrid 2222 |
. . . 4
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21 | funun 5255 |
. . . 4
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22 | 9, 20, 21 | syl2an 289 |
. . 3
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23 | 22 | 3impb 1199 |
. 2
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24 | df-tp 3599 |
. . 3
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25 | 24 | funeqi 5232 |
. 2
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26 | 23, 25 | sylibr 134 |
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 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-pw 3576 df-sn 3597 df-pr 3598 df-tp 3599 df-op 3600 df-br 4001 df-opab 4062 df-id 4289 df-xp 4628 df-rel 4629 df-cnv 4630 df-co 4631 df-dm 4632 df-fun 5213 |
This theorem is referenced by: fntp 5268 |
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