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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 2016 | . . 3 | |
2 | dfiota2 5148 | . . . 4 | |
3 | alnex 1486 | . . . . . . 7 | |
4 | ax-in2 605 | . . . . . . . . . 10 | |
5 | 4 | alimi 1442 | . . . . . . . . 9 |
6 | ss2ab 3205 | . . . . . . . . 9 | |
7 | 5, 6 | sylibr 133 | . . . . . . . 8 |
8 | dfnul2 3406 | . . . . . . . 8 | |
9 | 7, 8 | sseqtrrdi 3186 | . . . . . . 7 |
10 | 3, 9 | sylbir 134 | . . . . . 6 |
11 | 10 | unissd 3807 | . . . . 5 |
12 | uni0 3810 | . . . . 5 | |
13 | 11, 12 | sseqtrdi 3185 | . . . 4 |
14 | 2, 13 | eqsstrid 3183 | . . 3 |
15 | 1, 14 | sylnbi 668 | . 2 |
16 | ss0 3444 | . 2 | |
17 | 15, 16 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wal 1340 wceq 1342 wex 1479 weu 2013 cab 2150 wss 3111 c0 3404 cuni 3783 cio 5145 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-dif 3113 df-in 3117 df-ss 3124 df-nul 3405 df-sn 3576 df-uni 3784 df-iota 5147 |
This theorem is referenced by: tz6.12-2 5471 0fv 5515 riotaund 5826 |
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