Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > elnnz | Structured version Visualization version Unicode version |
Description: Positive integer property expressed in terms of integers. (Contributed by NM, 8-Jan-2002.) |
Ref | Expression |
---|---|
elnnz |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnre 11027 | . . . 4 | |
2 | orc 400 | . . . 4 | |
3 | nngt0 11049 | . . . 4 | |
4 | 1, 2, 3 | jca31 557 | . . 3 |
5 | idd 24 | . . . . . . 7 | |
6 | lt0neg2 10535 | . . . . . . . . . . . 12 | |
7 | renegcl 10344 | . . . . . . . . . . . . 13 | |
8 | 0re 10040 | . . . . . . . . . . . . 13 | |
9 | ltnsym 10135 | . . . . . . . . . . . . 13 | |
10 | 7, 8, 9 | sylancl 694 | . . . . . . . . . . . 12 |
11 | 6, 10 | sylbid 230 | . . . . . . . . . . 11 |
12 | 11 | imp 445 | . . . . . . . . . 10 |
13 | nngt0 11049 | . . . . . . . . . 10 | |
14 | 12, 13 | nsyl 135 | . . . . . . . . 9 |
15 | gt0ne0 10493 | . . . . . . . . . 10 | |
16 | 15 | neneqd 2799 | . . . . . . . . 9 |
17 | ioran 511 | . . . . . . . . 9 | |
18 | 14, 16, 17 | sylanbrc 698 | . . . . . . . 8 |
19 | 18 | pm2.21d 118 | . . . . . . 7 |
20 | 5, 19 | jaod 395 | . . . . . 6 |
21 | 20 | ex 450 | . . . . 5 |
22 | 21 | com23 86 | . . . 4 |
23 | 22 | imp31 448 | . . 3 |
24 | 4, 23 | impbii 199 | . 2 |
25 | elz 11379 | . . . 4 | |
26 | 3orrot 1044 | . . . . . 6 | |
27 | 3orass 1040 | . . . . . 6 | |
28 | 26, 27 | bitri 264 | . . . . 5 |
29 | 28 | anbi2i 730 | . . . 4 |
30 | 25, 29 | bitri 264 | . . 3 |
31 | 30 | anbi1i 731 | . 2 |
32 | 24, 31 | bitr4i 267 | 1 |
Copyright terms: Public domain | W3C validator |