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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 2299 | . . . . 5 | |
3 | nfcsb1v 3064 | . . . . . 6 | |
4 | nfcsb1v 3064 | . . . . . 6 | |
5 | 3, 4 | nfop 3759 | . . . . 5 |
6 | csbeq1a 3040 | . . . . . 6 | |
7 | csbeq1a 3040 | . . . . . 6 | |
8 | 6, 7 | opeq12d 3751 | . . . . 5 |
9 | 2, 5, 8 | cbvmpt 4061 | . . . 4 |
10 | 9 | rneqi 4816 | . . 3 |
11 | 1, 10 | eqtri 2178 | . 2 |
12 | flift.2 | . . . 4 | |
13 | 12 | ralrimiva 2530 | . . 3 |
14 | 3 | nfel1 2310 | . . . 4 |
15 | 6 | eleq1d 2226 | . . . 4 |
16 | 14, 15 | rspc 2810 | . . 3 |
17 | 13, 16 | mpan9 279 | . 2 |
18 | flift.3 | . . . 4 | |
19 | 18 | ralrimiva 2530 | . . 3 |
20 | 4 | nfel1 2310 | . . . 4 |
21 | 7 | eleq1d 2226 | . . . 4 |
22 | 20, 21 | rspc 2810 | . . 3 |
23 | 19, 22 | mpan9 279 | . 2 |
24 | csbeq1 3034 | . 2 | |
25 | csbeq1 3034 | . 2 | |
26 | 11, 17, 23, 24, 25 | fliftfun 5748 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wcel 2128 wral 2435 csb 3031 cop 3564 cmpt 4027 crn 4589 wfun 5166 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-sbc 2938 df-csb 3032 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-mpt 4029 df-id 4255 df-xp 4594 df-rel 4595 df-cnv 4596 df-co 4597 df-dm 4598 df-rn 4599 df-res 4600 df-ima 4601 df-iota 5137 df-fun 5174 df-fn 5175 df-f 5176 df-fv 5180 |
This theorem is referenced by: (None) |
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