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Mirrors > Home > ILE Home > Th. List > fliftfuns | Unicode version |
Description: The function is the unique function defined by , provided that the well-definedness condition holds. (Contributed by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
flift.1 | |
flift.2 | |
flift.3 |
Ref | Expression |
---|---|
fliftfuns |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | flift.1 | . . 3 | |
2 | nfcv 2178 | . . . . 5 | |
3 | nfcsb1v 2882 | . . . . . 6 | |
4 | nfcsb1v 2882 | . . . . . 6 | |
5 | 3, 4 | nfop 3565 | . . . . 5 |
6 | csbeq1a 2860 | . . . . . 6 | |
7 | csbeq1a 2860 | . . . . . 6 | |
8 | 6, 7 | opeq12d 3557 | . . . . 5 |
9 | 2, 5, 8 | cbvmpt 3851 | . . . 4 |
10 | 9 | rneqi 4562 | . . 3 |
11 | 1, 10 | eqtri 2060 | . 2 |
12 | flift.2 | . . . 4 | |
13 | 12 | ralrimiva 2392 | . . 3 |
14 | 3 | nfel1 2188 | . . . 4 |
15 | 6 | eleq1d 2106 | . . . 4 |
16 | 14, 15 | rspc 2650 | . . 3 |
17 | 13, 16 | mpan9 265 | . 2 |
18 | flift.3 | . . . 4 | |
19 | 18 | ralrimiva 2392 | . . 3 |
20 | 4 | nfel1 2188 | . . . 4 |
21 | 7 | eleq1d 2106 | . . . 4 |
22 | 20, 21 | rspc 2650 | . . 3 |
23 | 19, 22 | mpan9 265 | . 2 |
24 | csbeq1 2855 | . 2 | |
25 | csbeq1 2855 | . 2 | |
26 | 11, 17, 23, 24, 25 | fliftfun 5436 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wcel 1393 wral 2306 csb 2852 cop 3378 cmpt 3818 crn 4346 wfun 4896 |
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 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-rab 2315 df-v 2559 df-sbc 2765 df-csb 2853 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-mpt 3820 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-res 4357 df-ima 4358 df-iota 4867 df-fun 4904 df-fn 4905 df-f 4906 df-fv 4910 |
This theorem is referenced by: (None) |
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