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Mirrors > Home > ILE Home > Th. List > brprcneu | Unicode version |
Description: If is a proper class and is any class, then there is no unique set which is related to through the binary relation . (Contributed by Scott Fenton, 7-Oct-2017.) |
Ref | Expression |
---|---|
brprcneu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dtruex 4302 | . . . . . . . . 9 | |
2 | equcom 1633 | . . . . . . . . . . 11 | |
3 | 2 | notbii 626 | . . . . . . . . . 10 |
4 | 3 | exbii 1536 | . . . . . . . . 9 |
5 | 1, 4 | mpbir 144 | . . . . . . . 8 |
6 | 5 | jctr 308 | . . . . . . 7 |
7 | 19.42v 1827 | . . . . . . 7 | |
8 | 6, 7 | sylibr 132 | . . . . . 6 |
9 | opprc1 3592 | . . . . . . . 8 | |
10 | 9 | eleq1d 2147 | . . . . . . 7 |
11 | opprc1 3592 | . . . . . . . . . . . 12 | |
12 | 11 | eleq1d 2147 | . . . . . . . . . . 11 |
13 | 10, 12 | anbi12d 456 | . . . . . . . . . 10 |
14 | anidm 388 | . . . . . . . . . 10 | |
15 | 13, 14 | syl6bb 194 | . . . . . . . . 9 |
16 | 15 | anbi1d 452 | . . . . . . . 8 |
17 | 16 | exbidv 1746 | . . . . . . 7 |
18 | 10, 17 | imbi12d 232 | . . . . . 6 |
19 | 8, 18 | mpbiri 166 | . . . . 5 |
20 | df-br 3786 | . . . . 5 | |
21 | df-br 3786 | . . . . . . . 8 | |
22 | 20, 21 | anbi12i 447 | . . . . . . 7 |
23 | 22 | anbi1i 445 | . . . . . 6 |
24 | 23 | exbii 1536 | . . . . 5 |
25 | 19, 20, 24 | 3imtr4g 203 | . . . 4 |
26 | 25 | eximdv 1801 | . . 3 |
27 | exanaliim 1578 | . . . . . 6 | |
28 | 27 | eximi 1531 | . . . . 5 |
29 | exnalim 1577 | . . . . 5 | |
30 | 28, 29 | syl 14 | . . . 4 |
31 | breq2 3789 | . . . . . 6 | |
32 | 31 | mo4 2002 | . . . . 5 |
33 | 32 | notbii 626 | . . . 4 |
34 | 30, 33 | sylibr 132 | . . 3 |
35 | 26, 34 | syl6 33 | . 2 |
36 | eu5 1988 | . . . 4 | |
37 | 36 | notbii 626 | . . 3 |
38 | imnan 656 | . . 3 | |
39 | 37, 38 | bitr4i 185 | . 2 |
40 | 35, 39 | sylibr 132 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wal 1282 wex 1421 wcel 1433 weu 1941 wmo 1942 cvv 2601 c0 3251 cop 3401 class class class wbr 3785 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-setind 4280 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-ral 2353 df-v 2603 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-nul 3252 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 |
This theorem is referenced by: fvprc 5192 |
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