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Mirrors > Home > ILE Home > Th. List > isomni | Unicode version |
Description: The predicate of being omniscient. (Contributed by Jim Kingdon, 28-Jun-2022.) |
Ref | Expression |
---|---|
isomni | Omni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | feq2 5304 | . . . 4 | |
2 | rexeq 2653 | . . . . 5 | |
3 | raleq 2652 | . . . . 5 | |
4 | 2, 3 | orbi12d 783 | . . . 4 |
5 | 1, 4 | imbi12d 233 | . . 3 |
6 | 5 | albidv 1804 | . 2 |
7 | df-omni 7079 | . 2 Omni | |
8 | 6, 7 | elab2g 2859 | 1 Omni |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wo 698 wal 1333 wceq 1335 wcel 2128 wral 2435 wrex 2436 c0 3394 wf 5167 cfv 5171 c1o 6357 c2o 6358 Omnicomni 7078 |
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 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-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-fn 5174 df-f 5175 df-omni 7079 |
This theorem is referenced by: isomnimap 7081 finomni 7084 exmidomniim 7085 exmidomni 7086 omnimkv 7100 omniwomnimkv 7111 |
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