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Mirrors > Home > ILE Home > Th. List > iswomni | Unicode version |
Description: The predicate of being weakly omniscient. (Contributed by Jim Kingdon, 9-Jun-2024.) |
Ref | Expression |
---|---|
iswomni | WOmni DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | feq2 5303 | . . . 4 | |
2 | raleq 2652 | . . . . 5 | |
3 | 2 | dcbid 824 | . . . 4 DECID DECID |
4 | 1, 3 | imbi12d 233 | . . 3 DECID DECID |
5 | 4 | albidv 1804 | . 2 DECID DECID |
6 | df-womni 7107 | . 2 WOmni DECID | |
7 | 5, 6 | elab2g 2859 | 1 WOmni DECID |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 DECID wdc 820 wal 1333 wceq 1335 wcel 2128 wral 2435 wf 5166 cfv 5170 c1o 6356 c2o 6357 WOmnicwomni 7106 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-dc 821 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-v 2714 df-fn 5173 df-f 5174 df-womni 7107 |
This theorem is referenced by: iswomnimap 7109 omniwomnimkv 7110 |
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