Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > dmsnsnsng | Unicode version |
Description: The domain of the singleton of the singleton of a singleton. (Contributed by Jim Kingdon, 16-Dec-2018.) |
Ref | Expression |
---|---|
dmsnsnsng |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2663 | . . . . . . 7 | |
2 | 1 | opid 3693 | . . . . . 6 |
3 | sneq 3508 | . . . . . . 7 | |
4 | 3 | sneqd 3510 | . . . . . 6 |
5 | 2, 4 | syl5eq 2162 | . . . . 5 |
6 | 5 | sneqd 3510 | . . . 4 |
7 | 6 | dmeqd 4711 | . . 3 |
8 | 7, 3 | eqeq12d 2132 | . 2 |
9 | 1 | dmsnop 4982 | . 2 |
10 | 8, 9 | vtoclg 2720 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 wcel 1465 cvv 2660 csn 3497 cop 3500 cdm 4509 |
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 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-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-dm 4519 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |