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Mirrors > Home > ILE Home > Th. List > nn0cni | GIF version |
Description: A nonnegative integer is a complex number. (Contributed by NM, 14-May-2003.) |
Ref | Expression |
---|---|
nn0re.1 | ⊢ 𝐴 ∈ ℕ0 |
Ref | Expression |
---|---|
nn0cni | ⊢ 𝐴 ∈ ℂ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0re.1 | . . 3 ⊢ 𝐴 ∈ ℕ0 | |
2 | 1 | nn0rei 8956 | . 2 ⊢ 𝐴 ∈ ℝ |
3 | 2 | recni 7746 | 1 ⊢ 𝐴 ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 ℂcc 7586 ℕ0cn0 8945 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-cnex 7679 ax-resscn 7680 ax-1re 7682 ax-addrcl 7685 ax-rnegex 7697 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-int 3742 df-inn 8689 df-n0 8946 |
This theorem is referenced by: nn0le2xi 8995 num0u 9160 num0h 9161 numsuc 9163 numsucc 9189 numma 9193 nummac 9194 numma2c 9195 numadd 9196 numaddc 9197 nummul1c 9198 nummul2c 9199 decrmanc 9206 decrmac 9207 decaddi 9209 decaddci 9210 decsubi 9212 decmul1 9213 decmulnc 9216 11multnc 9217 decmul10add 9218 6p5lem 9219 4t3lem 9246 7t3e21 9259 7t6e42 9262 8t3e24 9265 8t4e32 9266 8t8e64 9270 9t3e27 9272 9t4e36 9273 9t5e45 9274 9t6e54 9275 9t7e63 9276 9t11e99 9279 decbin0 9289 decbin2 9290 sq10 10427 3dec 10429 3dvdsdec 11489 3dvds2dec 11490 3lcm2e6 11765 |
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