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Mirrors > Home > ILE Home > Th. List > shftfib | Unicode version |
Description: Value of a fiber of the
relation ![]() |
Ref | Expression |
---|---|
shftfval.1 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
shftfib |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | shftfval.1 |
. . . . . . 7
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2 | 1 | shftfval 10829 |
. . . . . 6
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3 | 2 | breqd 4014 |
. . . . 5
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4 | vex 2740 |
. . . . . 6
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5 | eleq1 2240 |
. . . . . . . 8
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6 | oveq1 5881 |
. . . . . . . . 9
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7 | 6 | breq1d 4013 |
. . . . . . . 8
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8 | 5, 7 | anbi12d 473 |
. . . . . . 7
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9 | breq2 4007 |
. . . . . . . 8
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10 | 9 | anbi2d 464 |
. . . . . . 7
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11 | eqid 2177 |
. . . . . . 7
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12 | 8, 10, 11 | brabg 4269 |
. . . . . 6
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13 | 4, 12 | mpan2 425 |
. . . . 5
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14 | 3, 13 | sylan9bb 462 |
. . . 4
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15 | ibar 301 |
. . . . 5
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16 | 15 | adantl 277 |
. . . 4
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17 | 14, 16 | bitr4d 191 |
. . 3
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18 | 17 | abbidv 2295 |
. 2
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19 | imasng 4993 |
. . 3
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20 | 19 | adantl 277 |
. 2
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21 | simpr 110 |
. . . 4
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22 | simpl 109 |
. . . 4
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23 | 21, 22 | subcld 8267 |
. . 3
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24 | imasng 4993 |
. . 3
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25 | 23, 24 | syl 14 |
. 2
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26 | 18, 20, 25 | 3eqtr4d 2220 |
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-13 2150 ax-14 2151 ax-ext 2159 ax-coll 4118 ax-sep 4121 ax-pow 4174 ax-pr 4209 ax-un 4433 ax-setind 4536 ax-resscn 7902 ax-1cn 7903 ax-icn 7905 ax-addcl 7906 ax-addrcl 7907 ax-mulcl 7908 ax-addcom 7910 ax-addass 7912 ax-distr 7914 ax-i2m1 7915 ax-0id 7918 ax-rnegex 7919 ax-cnre 7921 |
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-reu 2462 df-rab 2464 df-v 2739 df-sbc 2963 df-csb 3058 df-dif 3131 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-iun 3888 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 df-riota 5830 df-ov 5877 df-oprab 5878 df-mpo 5879 df-sub 8129 df-shft 10823 |
This theorem is referenced by: shftval 10833 |
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