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Mirrors > Home > ILE Home > Th. List > nn0sscn | GIF version |
Description: Nonnegative integers are a subset of the complex numbers.) (Contributed by NM, 9-May-2004.) |
Ref | Expression |
---|---|
nn0sscn | ⊢ ℕ0 ⊆ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0ssre 9110 | . 2 ⊢ ℕ0 ⊆ ℝ | |
2 | ax-resscn 7837 | . 2 ⊢ ℝ ⊆ ℂ | |
3 | 1, 2 | sstri 3147 | 1 ⊢ ℕ0 ⊆ ℂ |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 3112 ℂcc 7743 ℝcr 7744 ℕ0cn0 9106 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 ax-sep 4095 ax-cnex 7836 ax-resscn 7837 ax-1re 7839 ax-addrcl 7842 ax-rnegex 7854 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2724 df-un 3116 df-in 3118 df-ss 3125 df-sn 3577 df-int 3820 df-inn 8850 df-n0 9107 |
This theorem is referenced by: nn0cn 9116 nn0expcl 10460 fsumnn0cl 11334 fprodnn0cl 11543 eulerthlemrprm 12150 eulerthlema 12151 |
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