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Mirrors > Home > MPE Home > Th. List > snfi | Structured version Visualization version Unicode version |
Description: A singleton is finite. (Contributed by NM, 4-Nov-2002.) |
Ref | Expression |
---|---|
snfi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1onn 7719 | . . . 4 | |
2 | ensn1g 8021 | . . . 4 | |
3 | breq2 4657 | . . . . 5 | |
4 | 3 | rspcev 3309 | . . . 4 |
5 | 1, 2, 4 | sylancr 695 | . . 3 |
6 | snprc 4253 | . . . 4 | |
7 | en0 8019 | . . . . 5 | |
8 | peano1 7085 | . . . . . 6 | |
9 | breq2 4657 | . . . . . . 7 | |
10 | 9 | rspcev 3309 | . . . . . 6 |
11 | 8, 10 | mpan 706 | . . . . 5 |
12 | 7, 11 | sylbir 225 | . . . 4 |
13 | 6, 12 | sylbi 207 | . . 3 |
14 | 5, 13 | pm2.61i 176 | . 2 |
15 | isfi 7979 | . 2 | |
16 | 14, 15 | mpbir 221 | 1 |
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