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Mirrors > Home > ILE Home > Th. List > qliftfun | Unicode version |
Description: The function ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
qlift.1 |
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qlift.2 |
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qlift.3 |
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qlift.4 |
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qliftfun.4 |
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Ref | Expression |
---|---|
qliftfun |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | qlift.1 |
. . 3
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2 | qlift.2 |
. . . 4
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3 | qlift.3 |
. . . 4
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4 | qlift.4 |
. . . 4
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5 | 1, 2, 3, 4 | qliftlem 6607 |
. . 3
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6 | eceq1 6564 |
. . 3
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7 | qliftfun.4 |
. . 3
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8 | 1, 5, 2, 6, 7 | fliftfun 5791 |
. 2
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9 | 3 | adantr 276 |
. . . . . . . . . . 11
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10 | simpr 110 |
. . . . . . . . . . 11
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11 | 9, 10 | ercl 6540 |
. . . . . . . . . 10
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12 | 9, 10 | ercl2 6542 |
. . . . . . . . . 10
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13 | 11, 12 | jca 306 |
. . . . . . . . 9
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14 | 13 | ex 115 |
. . . . . . . 8
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15 | 14 | pm4.71rd 394 |
. . . . . . 7
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16 | 3 | adantr 276 |
. . . . . . . . 9
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17 | simprl 529 |
. . . . . . . . 9
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18 | 16, 17 | erth 6573 |
. . . . . . . 8
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19 | 18 | pm5.32da 452 |
. . . . . . 7
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20 | 15, 19 | bitrd 188 |
. . . . . 6
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21 | 20 | imbi1d 231 |
. . . . 5
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22 | impexp 263 |
. . . . 5
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23 | 21, 22 | bitrdi 196 |
. . . 4
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24 | 23 | 2albidv 1867 |
. . 3
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25 | r2al 2496 |
. . 3
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26 | 24, 25 | bitr4di 198 |
. 2
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27 | 8, 26 | bitr4d 191 |
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-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4206 ax-un 4430 |
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-csb 3058 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-mpt 4063 df-id 4290 df-xp 4629 df-rel 4630 df-cnv 4631 df-co 4632 df-dm 4633 df-rn 4634 df-res 4635 df-ima 4636 df-iota 5174 df-fun 5214 df-fn 5215 df-f 5216 df-fv 5220 df-er 6529 df-ec 6531 df-qs 6535 |
This theorem is referenced by: qliftfund 6612 qliftfuns 6613 |
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