Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 6500 | . . 3 |
6 | eceq1 6457 | . . 3 | |
7 | qliftfun.4 | . . 3 | |
8 | 1, 5, 2, 6, 7 | fliftfun 5690 | . 2 |
9 | 3 | adantr 274 | . . . . . . . . . . 11 |
10 | simpr 109 | . . . . . . . . . . 11 | |
11 | 9, 10 | ercl 6433 | . . . . . . . . . 10 |
12 | 9, 10 | ercl2 6435 | . . . . . . . . . 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 6466 | . . . . . . . 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 2452 | . . 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 2414 cvv 2681 cop 3525 class class class wbr 3924 cmpt 3984 crn 4535 wfun 5112 wer 6419 cec 6420 cqs 6421 |
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 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-sbc 2905 df-csb 2999 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-mpt 3986 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-res 4546 df-ima 4547 df-iota 5083 df-fun 5120 df-fn 5121 df-f 5122 df-fv 5126 df-er 6422 df-ec 6424 df-qs 6428 |
This theorem is referenced by: qliftfund 6505 qliftfuns 6506 |
Copyright terms: Public domain | W3C validator |