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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 9139 | . 2 | |
2 | ax-resscn 7866 | . 2 | |
3 | 1, 2 | sstri 3156 | 1 |
Colors of variables: wff set class |
Syntax hints: wss 3121 cc 7772 cr 7773 cn0 9135 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-sep 4107 ax-cnex 7865 ax-resscn 7866 ax-1re 7868 ax-addrcl 7871 ax-rnegex 7883 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3589 df-int 3832 df-inn 8879 df-n0 9136 |
This theorem is referenced by: nn0cn 9145 nn0expcl 10490 fsumnn0cl 11366 fprodnn0cl 11575 eulerthlemrprm 12183 eulerthlema 12184 |
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