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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 5463 |
. . . 4
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3 | funcnvcnv 5275 |
. . . 4
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4 | 1, 2, 3 | 3syl 17 |
. . 3
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5 | f1ocnv 5474 |
. . . . . . 7
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6 | 1, 5 | syl 14 |
. . . . . 6
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7 | f1of1 5460 |
. . . . . 6
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8 | 6, 7 | syl 14 |
. . . . 5
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9 | ssrab2 3240 |
. . . . 5
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10 | f1ores 5476 |
. . . . 5
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11 | 8, 9, 10 | sylancl 413 |
. . . 4
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12 | f1oresrab.1 |
. . . . . . 7
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13 | 12 | mptpreima 5122 |
. . . . . 6
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14 | f1oresrab.3 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | 14 | 3expia 1205 |
. . . . . . . . 9
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16 | 15 | alrimiv 1874 |
. . . . . . . 8
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17 | f1of 5461 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
18 | 1, 17 | syl 14 |
. . . . . . . . . 10
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19 | 12 | fmpt 5666 |
. . . . . . . . . 10
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20 | 18, 19 | sylibr 134 |
. . . . . . . . 9
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21 | 20 | r19.21bi 2565 |
. . . . . . . 8
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22 | elrab3t 2892 |
. . . . . . . 8
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23 | 16, 21, 22 | syl2anc 411 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 23 | rabbidva 2725 |
. . . . . 6
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25 | 13, 24 | eqtrid 2222 |
. . . . 5
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26 | f1oeq3 5451 |
. . . . 5
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27 | 25, 26 | syl 14 |
. . . 4
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28 | 11, 27 | mpbid 147 |
. . 3
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29 | f1orescnv 5477 |
. . 3
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30 | 4, 28, 29 | syl2anc 411 |
. 2
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31 | rescnvcnv 5091 |
. . 3
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32 | f1oeq1 5449 |
. . 3
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33 | 31, 32 | ax-mp 5 |
. 2
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34 | 30, 33 | sylib 122 |
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-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 4121 ax-pow 4174 ax-pr 4209 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 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-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4004 df-opab 4065 df-mpt 4066 df-id 4293 df-xp 4632 df-rel 4633 df-cnv 4634 df-co 4635 df-dm 4636 df-rn 4637 df-res 4638 df-ima 4639 df-iota 5178 df-fun 5218 df-fn 5219 df-f 5220 df-f1 5221 df-fo 5222 df-f1o 5223 df-fv 5224 |
This theorem is referenced by: (None) |
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