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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 4444 | . . . . . . . . 9 | |
2 | equcom 1667 | . . . . . . . . . . 11 | |
3 | 2 | notbii 642 | . . . . . . . . . 10 |
4 | 3 | exbii 1569 | . . . . . . . . 9 |
5 | 1, 4 | mpbir 145 | . . . . . . . 8 |
6 | 5 | jctr 313 | . . . . . . 7 |
7 | 19.42v 1862 | . . . . . . 7 | |
8 | 6, 7 | sylibr 133 | . . . . . 6 |
9 | opprc1 3697 | . . . . . . . 8 | |
10 | 9 | eleq1d 2186 | . . . . . . 7 |
11 | opprc1 3697 | . . . . . . . . . . . 12 | |
12 | 11 | eleq1d 2186 | . . . . . . . . . . 11 |
13 | 10, 12 | anbi12d 464 | . . . . . . . . . 10 |
14 | anidm 393 | . . . . . . . . . 10 | |
15 | 13, 14 | syl6bb 195 | . . . . . . . . 9 |
16 | 15 | anbi1d 460 | . . . . . . . 8 |
17 | 16 | exbidv 1781 | . . . . . . 7 |
18 | 10, 17 | imbi12d 233 | . . . . . 6 |
19 | 8, 18 | mpbiri 167 | . . . . 5 |
20 | df-br 3900 | . . . . 5 | |
21 | df-br 3900 | . . . . . . . 8 | |
22 | 20, 21 | anbi12i 455 | . . . . . . 7 |
23 | 22 | anbi1i 453 | . . . . . 6 |
24 | 23 | exbii 1569 | . . . . 5 |
25 | 19, 20, 24 | 3imtr4g 204 | . . . 4 |
26 | 25 | eximdv 1836 | . . 3 |
27 | exanaliim 1611 | . . . . . 6 | |
28 | 27 | eximi 1564 | . . . . 5 |
29 | exnalim 1610 | . . . . 5 | |
30 | 28, 29 | syl 14 | . . . 4 |
31 | breq2 3903 | . . . . . 6 | |
32 | 31 | mo4 2038 | . . . . 5 |
33 | 32 | notbii 642 | . . . 4 |
34 | 30, 33 | sylibr 133 | . . 3 |
35 | 26, 34 | syl6 33 | . 2 |
36 | eu5 2024 | . . . 4 | |
37 | 36 | notbii 642 | . . 3 |
38 | imnan 664 | . . 3 | |
39 | 37, 38 | bitr4i 186 | . 2 |
40 | 35, 39 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wal 1314 wex 1453 wcel 1465 weu 1977 wmo 1978 cvv 2660 c0 3333 cop 3500 class class class wbr 3899 |
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-in1 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-setind 4422 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-ral 2398 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 |
This theorem is referenced by: fvprc 5383 |
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