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Mirrors > Home > MPE Home > Th. List > nnnn0i | Structured version Visualization version Unicode version |
Description: A positive integer is a nonnegative integer. (Contributed by NM, 20-Jun-2005.) |
Ref | Expression |
---|---|
nnnn0i.1 |
Ref | Expression |
---|---|
nnnn0i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnnn0i.1 | . 2 | |
2 | nnnn0 11299 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1990 cn 11020 cn0 11292 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 df-in 3581 df-ss 3588 df-n0 11293 |
This theorem is referenced by: 1nn0 11308 2nn0 11309 3nn0 11310 4nn0 11311 5nn0 11312 6nn0 11313 7nn0 11314 8nn0 11315 9nn0 11316 10nn0OLD 11317 numlt 11527 declei 11542 numlti 11545 faclbnd4lem1 13080 divalglem6 15121 pockthi 15611 dec5dvds2 15769 modxp1i 15774 mod2xnegi 15775 43prm 15829 83prm 15830 317prm 15833 strlemor2OLD 15970 strlemor3OLD 15971 log2ublem2 24674 rpdp2cl2 29590 ballotlemfmpn 30556 ballotth 30599 circlevma 30720 tgblthelfgott 41703 tgoldbach 41705 bgoldbachltOLD 41707 tgblthelfgottOLD 41709 tgoldbachOLD 41712 |
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