Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nn0sscn | Unicode version |
Description: Nonnegative integers are a subset of the complex numbers.) (Contributed by NM, 9-May-2004.) |
Ref | Expression |
---|---|
nn0sscn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0ssre 9094 | . 2 | |
2 | ax-resscn 7824 | . 2 | |
3 | 1, 2 | sstri 3137 | 1 |
Colors of variables: wff set class |
Syntax hints: wss 3102 cc 7730 cr 7731 cn0 9090 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 ax-sep 4082 ax-cnex 7823 ax-resscn 7824 ax-1re 7826 ax-addrcl 7829 ax-rnegex 7841 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3566 df-int 3808 df-inn 8834 df-n0 9091 |
This theorem is referenced by: nn0cn 9100 nn0expcl 10433 fsumnn0cl 11300 fprodnn0cl 11509 eulerthlemrprm 12103 eulerthlema 12104 |
Copyright terms: Public domain | W3C validator |