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Mirrors > Home > ILE Home > Th. List > iotanul | Unicode version |
Description: Theorem 8.22 in [Quine] p. 57. This theorem is the result if there isn't exactly one that satisfies . (Contributed by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
iotanul |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 1903 | . . 3 | |
2 | dfiota2 4868 | . . . 4 | |
3 | alnex 1388 | . . . . . . 7 | |
4 | ax-in2 545 | . . . . . . . . . 10 | |
5 | 4 | alimi 1344 | . . . . . . . . 9 |
6 | ss2ab 3008 | . . . . . . . . 9 | |
7 | 5, 6 | sylibr 137 | . . . . . . . 8 |
8 | dfnul2 3226 | . . . . . . . 8 | |
9 | 7, 8 | syl6sseqr 2992 | . . . . . . 7 |
10 | 3, 9 | sylbir 125 | . . . . . 6 |
11 | 10 | unissd 3604 | . . . . 5 |
12 | uni0 3607 | . . . . 5 | |
13 | 11, 12 | syl6sseq 2991 | . . . 4 |
14 | 2, 13 | syl5eqss 2989 | . . 3 |
15 | 1, 14 | sylnbi 603 | . 2 |
16 | ss0 3257 | . 2 | |
17 | 15, 16 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 98 wal 1241 wceq 1243 wex 1381 weu 1900 cab 2026 wss 2917 c0 3224 cuni 3580 cio 4865 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-eu 1903 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-dif 2920 df-in 2924 df-ss 2931 df-nul 3225 df-sn 3381 df-uni 3581 df-iota 4867 |
This theorem is referenced by: tz6.12-2 5169 0fv 5208 riotaund 5502 |
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