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Mirrors > Home > ILE Home > Th. List > f1oresrab | Unicode version |
Description: Build a bijection between restricted abstract builders, given a bijection between the base classes, deduction version. (Contributed by Thierry Arnoux, 17-Aug-2018.) |
Ref | Expression |
---|---|
f1oresrab.1 |
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f1oresrab.2 |
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f1oresrab.3 |
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Ref | Expression |
---|---|
f1oresrab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1oresrab.2 |
. . . 4
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2 | f1ofun 5377 |
. . . 4
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3 | funcnvcnv 5190 |
. . . 4
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4 | 1, 2, 3 | 3syl 17 |
. . 3
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5 | f1ocnv 5388 |
. . . . . . 7
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6 | 1, 5 | syl 14 |
. . . . . 6
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7 | f1of1 5374 |
. . . . . 6
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8 | 6, 7 | syl 14 |
. . . . 5
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9 | ssrab2 3187 |
. . . . 5
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10 | f1ores 5390 |
. . . . 5
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11 | 8, 9, 10 | sylancl 410 |
. . . 4
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12 | f1oresrab.1 |
. . . . . . 7
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13 | 12 | mptpreima 5040 |
. . . . . 6
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14 | f1oresrab.3 |
. . . . . . . . . 10
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15 | 14 | 3expia 1184 |
. . . . . . . . 9
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16 | 15 | alrimiv 1847 |
. . . . . . . 8
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17 | f1of 5375 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
18 | 1, 17 | syl 14 |
. . . . . . . . . 10
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19 | 12 | fmpt 5578 |
. . . . . . . . . 10
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20 | 18, 19 | sylibr 133 |
. . . . . . . . 9
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21 | 20 | r19.21bi 2523 |
. . . . . . . 8
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22 | elrab3t 2843 |
. . . . . . . 8
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23 | 16, 21, 22 | syl2anc 409 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 23 | rabbidva 2677 |
. . . . . 6
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25 | 13, 24 | syl5eq 2185 |
. . . . 5
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26 | f1oeq3 5366 |
. . . . 5
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27 | 25, 26 | syl 14 |
. . . 4
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28 | 11, 27 | mpbid 146 |
. . 3
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29 | f1orescnv 5391 |
. . 3
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30 | 4, 28, 29 | syl2anc 409 |
. 2
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31 | rescnvcnv 5009 |
. . 3
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32 | f1oeq1 5364 |
. . 3
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33 | 31, 32 | ax-mp 5 |
. 2
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34 | 30, 33 | sylib 121 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-sbc 2914 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-mpt 3999 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 df-iota 5096 df-fun 5133 df-fn 5134 df-f 5135 df-f1 5136 df-fo 5137 df-f1o 5138 df-fv 5139 |
This theorem is referenced by: (None) |
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