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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 3152 | . 2 | |
2 | riotacl2 5711 | . 2 | |
3 | 1, 2 | sseldi 3065 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1465 wreu 2395 crab 2397 crio 5697 |
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-eu 1980 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-reu 2400 df-rab 2402 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-uni 3707 df-iota 5058 df-riota 5698 |
This theorem is referenced by: riotaprop 5721 riotass2 5724 riotass 5725 acexmidlemcase 5737 supclti 6853 caucvgsrlemcl 7565 caucvgsrlemgt1 7571 axcaucvglemcl 7671 subval 7922 subcl 7929 divvalap 8402 divclap 8406 lbcl 8672 divfnzn 9381 flqcl 10014 flapcl 10016 cjval 10585 cjth 10586 cjf 10587 oddpwdclemodd 11777 oddpwdclemdc 11778 oddpwdc 11779 qnumdencl 11792 qnumdenbi 11797 |
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