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Mirrors > Home > ILE Home > Th. List > qliftfun | 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 |
---|---|
qlift.1 | |
qlift.2 | |
qlift.3 | |
qlift.4 | |
qliftfun.4 |
Ref | Expression |
---|---|
qliftfun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | qlift.1 | . . 3 | |
2 | qlift.2 | . . . 4 | |
3 | qlift.3 | . . . 4 | |
4 | qlift.4 | . . . 4 | |
5 | 1, 2, 3, 4 | qliftlem 6507 | . . 3 |
6 | eceq1 6464 | . . 3 | |
7 | qliftfun.4 | . . 3 | |
8 | 1, 5, 2, 6, 7 | fliftfun 5697 | . 2 |
9 | 3 | adantr 274 | . . . . . . . . . . 11 |
10 | simpr 109 | . . . . . . . . . . 11 | |
11 | 9, 10 | ercl 6440 | . . . . . . . . . 10 |
12 | 9, 10 | ercl2 6442 | . . . . . . . . . 10 |
13 | 11, 12 | jca 304 | . . . . . . . . 9 |
14 | 13 | ex 114 | . . . . . . . 8 |
15 | 14 | pm4.71rd 391 | . . . . . . 7 |
16 | 3 | adantr 274 | . . . . . . . . 9 |
17 | simprl 520 | . . . . . . . . 9 | |
18 | 16, 17 | erth 6473 | . . . . . . . 8 |
19 | 18 | pm5.32da 447 | . . . . . . 7 |
20 | 15, 19 | bitrd 187 | . . . . . 6 |
21 | 20 | imbi1d 230 | . . . . 5 |
22 | impexp 261 | . . . . 5 | |
23 | 21, 22 | syl6bb 195 | . . . 4 |
24 | 23 | 2albidv 1839 | . . 3 |
25 | r2al 2454 | . . 3 | |
26 | 24, 25 | syl6bbr 197 | . 2 |
27 | 8, 26 | bitr4d 190 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wceq 1331 wcel 1480 wral 2416 cvv 2686 cop 3530 class class class wbr 3929 cmpt 3989 crn 4540 wfun 5117 wer 6426 cec 6427 cqs 6428 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-rab 2425 df-v 2688 df-sbc 2910 df-csb 3004 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-fv 5131 df-er 6429 df-ec 6431 df-qs 6435 |
This theorem is referenced by: qliftfund 6512 qliftfuns 6513 |
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