Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 4474 | . . . . . . . . 9 | |
2 | equcom 1682 | . . . . . . . . . . 11 | |
3 | 2 | notbii 657 | . . . . . . . . . 10 |
4 | 3 | exbii 1584 | . . . . . . . . 9 |
5 | 1, 4 | mpbir 145 | . . . . . . . 8 |
6 | 5 | jctr 313 | . . . . . . 7 |
7 | 19.42v 1878 | . . . . . . 7 | |
8 | 6, 7 | sylibr 133 | . . . . . 6 |
9 | opprc1 3727 | . . . . . . . 8 | |
10 | 9 | eleq1d 2208 | . . . . . . 7 |
11 | opprc1 3727 | . . . . . . . . . . . 12 | |
12 | 11 | eleq1d 2208 | . . . . . . . . . . 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 1797 | . . . . . . 7 |
18 | 10, 17 | imbi12d 233 | . . . . . 6 |
19 | 8, 18 | mpbiri 167 | . . . . 5 |
20 | df-br 3930 | . . . . 5 | |
21 | df-br 3930 | . . . . . . . 8 | |
22 | 20, 21 | anbi12i 455 | . . . . . . 7 |
23 | 22 | anbi1i 453 | . . . . . 6 |
24 | 23 | exbii 1584 | . . . . 5 |
25 | 19, 20, 24 | 3imtr4g 204 | . . . 4 |
26 | 25 | eximdv 1852 | . . 3 |
27 | exanaliim 1626 | . . . . . 6 | |
28 | 27 | eximi 1579 | . . . . 5 |
29 | exnalim 1625 | . . . . 5 | |
30 | 28, 29 | syl 14 | . . . 4 |
31 | breq2 3933 | . . . . . 6 | |
32 | 31 | mo4 2060 | . . . . 5 |
33 | 32 | notbii 657 | . . . 4 |
34 | 30, 33 | sylibr 133 | . . 3 |
35 | 26, 34 | syl6 33 | . 2 |
36 | eu5 2046 | . . . 4 | |
37 | 36 | notbii 657 | . . 3 |
38 | imnan 679 | . . 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 1329 wex 1468 wcel 1480 weu 1999 wmo 2000 cvv 2686 c0 3363 cop 3530 class class class wbr 3929 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-setind 4452 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-ral 2421 df-v 2688 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 |
This theorem is referenced by: fvprc 5415 |
Copyright terms: Public domain | W3C validator |