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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 5071 |
. . . 4
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3 | funcnvcnv 4901 |
. . . 4
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4 | 1, 2, 3 | 3syl 17 |
. . 3
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5 | f1ocnv 5082 |
. . . . . . 7
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6 | 1, 5 | syl 14 |
. . . . . 6
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7 | f1of1 5068 |
. . . . . 6
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8 | 6, 7 | syl 14 |
. . . . 5
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9 | ssrab2 3019 |
. . . . 5
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10 | f1ores 5084 |
. . . . 5
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11 | 8, 9, 10 | sylancl 392 |
. . . 4
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12 | f1oresrab.1 |
. . . . . . 7
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13 | 12 | mptpreima 4757 |
. . . . . 6
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14 | f1oresrab.3 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | 14 | 3expia 1105 |
. . . . . . . . 9
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16 | 15 | alrimiv 1751 |
. . . . . . . 8
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17 | f1of 5069 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
18 | 1, 17 | syl 14 |
. . . . . . . . . 10
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19 | 12 | fmpt 5262 |
. . . . . . . . . 10
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20 | 18, 19 | sylibr 137 |
. . . . . . . . 9
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21 | 20 | r19.21bi 2401 |
. . . . . . . 8
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22 | elrab3t 2691 |
. . . . . . . 8
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23 | 16, 21, 22 | syl2anc 391 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 23 | rabbidva 2542 |
. . . . . 6
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25 | 13, 24 | syl5eq 2081 |
. . . . 5
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26 | f1oeq3 5062 |
. . . . 5
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27 | 25, 26 | syl 14 |
. . . 4
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28 | 11, 27 | mpbid 135 |
. . 3
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29 | f1orescnv 5085 |
. . 3
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30 | 4, 28, 29 | syl2anc 391 |
. 2
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31 | rescnvcnv 4726 |
. . 3
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32 | f1oeq1 5060 |
. . 3
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33 | 31, 32 | ax-mp 7 |
. 2
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34 | 30, 33 | sylib 127 |
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-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-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-rab 2309 df-v 2553 df-sbc 2759 df-un 2916 df-in 2918 df-ss 2925 df-pw 3353 df-sn 3373 df-pr 3374 df-op 3376 df-uni 3572 df-br 3756 df-opab 3810 df-mpt 3811 df-id 4021 df-xp 4294 df-rel 4295 df-cnv 4296 df-co 4297 df-dm 4298 df-rn 4299 df-res 4300 df-ima 4301 df-iota 4810 df-fun 4847 df-fn 4848 df-f 4849 df-f1 4850 df-fo 4851 df-f1o 4852 df-fv 4853 |
This theorem is referenced by: (None) |
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