Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 8299 | . 2 ⊢ 𝐴 ∈ ℝ |
3 | 2 | recni 7131 | 1 ⊢ 𝐴 ∈ ℂ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1433 ℂcc 6979 ℕ0cn0 8288 |
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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-cnex 7067 ax-resscn 7068 ax-1re 7070 ax-addrcl 7073 ax-rnegex 7085 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-int 3637 df-inn 8040 df-n0 8289 |
This theorem is referenced by: nn0le2xi 8338 num0u 8487 num0h 8488 numsuc 8490 numsucc 8516 numma 8520 nummac 8521 numma2c 8522 numadd 8523 numaddc 8524 nummul1c 8525 nummul2c 8526 decrmanc 8533 decrmac 8534 decaddi 8536 decaddci 8537 decsubi 8539 decmul1 8540 decmulnc 8543 11multnc 8544 decmul10add 8545 6p5lem 8546 4t3lem 8573 7t3e21 8586 7t6e42 8589 8t3e24 8592 8t4e32 8593 8t8e64 8597 9t3e27 8599 9t4e36 8600 9t5e45 8601 9t6e54 8602 9t7e63 8603 9t11e99 8606 decbin0 8616 decbin2 8617 sq10 9640 3dec 9642 3dvdsdec 10264 3dvds2dec 10265 3lcm2e6 10539 |
Copyright terms: Public domain | W3C validator |