Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > riotacl | Structured version Visualization version Unicode version |
Description: Closure of restricted iota. (Contributed by NM, 21-Aug-2011.) |
Ref | Expression |
---|---|
riotacl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssrab2 3687 | . 2 | |
2 | riotacl2 6624 | . 2 | |
3 | 1, 2 | sseldi 3601 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 wreu 2914 crab 2916 crio 6610 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-un 3579 df-in 3581 df-ss 3588 df-sn 4178 df-pr 4180 df-uni 4437 df-iota 5851 df-riota 6611 |
This theorem is referenced by: riotaeqimp 6634 riotaprop 6635 riotass2 6638 riotass 6639 riotaxfrd 6642 riotaclb 6649 supcl 8364 fisupcl 8375 htalem 8759 dfac8clem 8855 dfac2a 8952 fin23lem22 9149 zorn2lem1 9318 subcl 10280 divcl 10691 lbcl 10974 flcl 12596 cjf 13844 sqrtcl 14101 qnumdencl 15447 qnumdenbi 15452 catidcl 16343 lubcl 16985 glbcl 16998 ismgmid 17264 grpinvf 17466 pj1f 18110 mirf 25555 midf 25668 ismidb 25670 lmif 25677 islmib 25679 uspgredg2vlem 26115 usgredg2vlem1 26117 frgrncvvdeqlem4 27166 grpoidcl 27368 grpoinvcl 27378 pjpreeq 28257 cnlnadjlem3 28928 adjbdln 28942 xdivcld 29631 cvmlift3lem3 31303 nosupno 31849 nosupbday 31851 nosupbnd1 31860 scutcut 31912 transportcl 32140 finxpreclem4 33231 poimirlem26 33435 iorlid 33657 riotaclbgBAD 34240 lshpkrlem2 34398 lshpkrcl 34403 cdleme25cl 35645 cdleme29cl 35665 cdlemefrs29clN 35687 cdlemk29-3 36199 cdlemkid5 36223 dihlsscpre 36523 mapdhcl 37016 hdmapcl 37122 hgmapcl 37181 wessf1ornlem 39371 fourierdlem50 40373 |
Copyright terms: Public domain | W3C validator |