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Mirrors > Home > MPE Home > Th. List > elfz2nn0 | Structured version Visualization version Unicode version |
Description: Membership in a finite set of sequential nonnegative integers. (Contributed by NM, 16-Sep-2005.) (Revised by Mario Carneiro, 28-Apr-2015.) |
Ref | Expression |
---|---|
elfz2nn0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elnn0uz 11725 | . . . 4 | |
2 | 1 | anbi1i 731 | . . 3 |
3 | eluznn0 11757 | . . . . . 6 | |
4 | eluzle 11700 | . . . . . . 7 | |
5 | 4 | adantl 482 | . . . . . 6 |
6 | 3, 5 | jca 554 | . . . . 5 |
7 | nn0z 11400 | . . . . . . . 8 | |
8 | nn0z 11400 | . . . . . . . 8 | |
9 | eluz 11701 | . . . . . . . 8 | |
10 | 7, 8, 9 | syl2an 494 | . . . . . . 7 |
11 | 10 | biimprd 238 | . . . . . 6 |
12 | 11 | impr 649 | . . . . 5 |
13 | 6, 12 | impbida 877 | . . . 4 |
14 | 13 | pm5.32i 669 | . . 3 |
15 | 2, 14 | bitr3i 266 | . 2 |
16 | elfzuzb 12336 | . 2 | |
17 | 3anass 1042 | . 2 | |
18 | 15, 16, 17 | 3bitr4i 292 | 1 |
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