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Mirrors > Home > ILE Home > Th. List > ordunisuc2r | Unicode version |
Description: An ordinal which contains the successor of each of its members is equal to its union. (Contributed by Jim Kingdon, 14-Nov-2018.) |
Ref | Expression |
---|---|
ordunisuc2r |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2663 | . . . . . . . . 9 | |
2 | 1 | sucid 4309 | . . . . . . . 8 |
3 | elunii 3711 | . . . . . . . 8 | |
4 | 2, 3 | mpan 420 | . . . . . . 7 |
5 | 4 | imim2i 12 | . . . . . 6 |
6 | 5 | alimi 1416 | . . . . 5 |
7 | df-ral 2398 | . . . . 5 | |
8 | dfss2 3056 | . . . . 5 | |
9 | 6, 7, 8 | 3imtr4i 200 | . . . 4 |
10 | 9 | a1i 9 | . . 3 |
11 | orduniss 4317 | . . 3 | |
12 | 10, 11 | jctird 315 | . 2 |
13 | eqss 3082 | . 2 | |
14 | 12, 13 | syl6ibr 161 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1314 wceq 1316 wcel 1465 wral 2393 wss 3041 cuni 3706 word 4254 csuc 4257 |
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-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-uni 3707 df-tr 3997 df-iord 4258 df-suc 4263 |
This theorem is referenced by: (None) |
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