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Mirrors > Home > ILE Home > Th. List > riotacl | Unicode version |
Description: Closure of restricted iota. (Contributed by NM, 21-Aug-2011.) |
Ref | Expression |
---|---|
riotacl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssrab2 3025 | . 2 | |
2 | riotacl2 5481 | . 2 | |
3 | 1, 2 | sseldi 2943 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1393 wreu 2308 crab 2310 crio 5467 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-reu 2313 df-rab 2315 df-v 2559 df-sbc 2765 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-uni 3581 df-iota 4867 df-riota 5468 |
This theorem is referenced by: riotaprop 5491 riotass2 5494 riotass 5495 acexmidlemcase 5507 caucvgsrlemcl 6873 caucvgsrlemgt1 6879 axcaucvglemcl 6969 subval 7203 subcl 7210 divvalap 7653 divclap 7657 divfnzn 8556 flqcl 9117 cjval 9445 cjth 9446 cjf 9447 |
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