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Mirrors > Home > ILE Home > Th. List > recn | Unicode version |
Description: A real number is a complex number. (Contributed by NM, 10-Aug-1999.) |
Ref | Expression |
---|---|
recn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-resscn 7068 | . 2 | |
2 | 1 | sseli 2995 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1433 cc 6979 cr 6980 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-resscn 7068 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-in 2979 df-ss 2986 |
This theorem is referenced by: mulid1 7116 recnd 7147 pnfnre 7160 mnfnre 7161 cnegexlem1 7283 cnegexlem2 7284 cnegexlem3 7285 cnegex 7286 renegcl 7369 resubcl 7372 negf1o 7486 mul02lem2 7492 ltaddneg 7528 ltaddnegr 7529 ltaddsub2 7541 leaddsub2 7543 leltadd 7551 ltaddpos 7556 ltaddpos2 7557 posdif 7559 lenegcon1 7570 lenegcon2 7571 addge01 7576 addge02 7577 leaddle0 7581 mullt0 7584 recexre 7678 msqge0 7716 mulge0 7719 recexap 7743 ltm1 7924 prodgt02 7931 prodge02 7933 ltmul2 7934 lemul2 7935 lemul2a 7937 ltmulgt12 7943 lemulge12 7945 gt0div 7948 ge0div 7949 ltmuldiv2 7953 ltdivmul 7954 ltdivmul2 7956 ledivmul2 7958 lemuldiv2 7960 negiso 8033 cju 8038 nnge1 8062 halfpos 8262 lt2halves 8266 addltmul 8267 avgle1 8271 avgle2 8272 div4p1lem1div2 8284 nnrecl 8286 elznn0 8366 elznn 8367 nzadd 8403 zmulcl 8404 elz2 8419 gtndiv 8442 zeo 8452 supminfex 8685 eqreznegel 8699 negm 8700 irradd 8731 irrmul 8732 divlt1lt 8801 divle1le 8802 xnegneg 8900 divelunit 9024 fzonmapblen 9196 expgt1 9514 mulexpzap 9516 leexp1a 9531 expubnd 9533 sqgt0ap 9544 lt2sq 9549 le2sq 9550 sqge0 9552 sumsqeq0 9554 bernneq 9593 bernneq2 9594 crre 9744 crim 9745 reim0 9748 mulreap 9751 rere 9752 remul2 9760 redivap 9761 immul2 9767 imdivap 9768 cjre 9769 cjreim 9790 rennim 9888 sqrt0rlem 9889 resqrexlemover 9896 absreimsq 9953 absreim 9954 absnid 9959 leabs 9960 absre 9963 absresq 9964 sqabs 9968 ltabs 9973 absdiflt 9978 absdifle 9979 lenegsq 9981 abssuble0 9989 dfabsmax 10103 max0addsup 10105 negfi 10110 odd2np1 10272 infssuzex 10345 |
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