Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2312 | . . . . 5 | |
3 | nfcsb1v 3082 | . . . . . 6 | |
4 | nfcsb1v 3082 | . . . . . 6 | |
5 | 3, 4 | nfop 3781 | . . . . 5 |
6 | csbeq1a 3058 | . . . . . 6 | |
7 | csbeq1a 3058 | . . . . . 6 | |
8 | 6, 7 | opeq12d 3773 | . . . . 5 |
9 | 2, 5, 8 | cbvmpt 4084 | . . . 4 |
10 | 9 | rneqi 4839 | . . 3 |
11 | 1, 10 | eqtri 2191 | . 2 |
12 | flift.2 | . . . 4 | |
13 | 12 | ralrimiva 2543 | . . 3 |
14 | 3 | nfel1 2323 | . . . 4 |
15 | 6 | eleq1d 2239 | . . . 4 |
16 | 14, 15 | rspc 2828 | . . 3 |
17 | 13, 16 | mpan9 279 | . 2 |
18 | flift.3 | . . . 4 | |
19 | 18 | ralrimiva 2543 | . . 3 |
20 | 4 | nfel1 2323 | . . . 4 |
21 | 7 | eleq1d 2239 | . . . 4 |
22 | 20, 21 | rspc 2828 | . . 3 |
23 | 19, 22 | mpan9 279 | . 2 |
24 | csbeq1 3052 | . 2 | |
25 | csbeq1 3052 | . 2 | |
26 | 11, 17, 23, 24, 25 | fliftfun 5775 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wcel 2141 wral 2448 csb 3049 cop 3586 cmpt 4050 crn 4612 wfun 5192 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-rab 2457 df-v 2732 df-sbc 2956 df-csb 3050 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-opab 4051 df-mpt 4052 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-rn 4622 df-res 4623 df-ima 4624 df-iota 5160 df-fun 5200 df-fn 5201 df-f 5202 df-fv 5206 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |