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Mirrors > Home > ILE Home > Th. List > f1ofveu | Unicode version |
Description: There is one domain element for each value of a one-to-one onto function. (Contributed by NM, 26-May-2006.) |
Ref | Expression |
---|---|
f1ofveu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1ocnv 5139 | . . . 4 | |
2 | f1of 5126 | . . . 4 | |
3 | 1, 2 | syl 14 | . . 3 |
4 | feu 5072 | . . 3 | |
5 | 3, 4 | sylan 267 | . 2 |
6 | f1ocnvfvb 5420 | . . . . . 6 | |
7 | 6 | 3com23 1110 | . . . . 5 |
8 | dff1o4 5134 | . . . . . . 7 | |
9 | 8 | simprbi 260 | . . . . . 6 |
10 | fnopfvb 5215 | . . . . . . 7 | |
11 | 10 | 3adant3 924 | . . . . . 6 |
12 | 9, 11 | syl3an1 1168 | . . . . 5 |
13 | 7, 12 | bitrd 177 | . . . 4 |
14 | 13 | 3expa 1104 | . . 3 |
15 | 14 | reubidva 2492 | . 2 |
16 | 5, 15 | mpbird 156 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 wceq 1243 wcel 1393 wreu 2308 cop 3378 ccnv 4344 wfn 4897 wf 4898 wf1o 4901 cfv 4902 |
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-reu 2313 df-v 2559 df-sbc 2765 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-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-f1 4907 df-fo 4908 df-f1o 4909 df-fv 4910 |
This theorem is referenced by: (None) |
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