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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 5331 | . . . 4 | |
2 | raleq 2665 | . . . . 5 | |
3 | 2 | dcbid 833 | . . . 4 DECID DECID |
4 | 1, 3 | imbi12d 233 | . . 3 DECID DECID |
5 | 4 | albidv 1817 | . 2 DECID DECID |
6 | df-womni 7140 | . 2 WOmni DECID | |
7 | 5, 6 | elab2g 2877 | 1 WOmni DECID |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 DECID wdc 829 wal 1346 wceq 1348 wcel 2141 wral 2448 wf 5194 cfv 5198 c1o 6388 c2o 6389 WOmnicwomni 7139 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-dc 830 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-v 2732 df-fn 5201 df-f 5202 df-womni 7140 |
This theorem is referenced by: iswomnimap 7142 omniwomnimkv 7143 |
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