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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 2002 | . . 3 | |
2 | dfiota2 5089 | . . . 4 | |
3 | alnex 1475 | . . . . . . 7 | |
4 | ax-in2 604 | . . . . . . . . . 10 | |
5 | 4 | alimi 1431 | . . . . . . . . 9 |
6 | ss2ab 3165 | . . . . . . . . 9 | |
7 | 5, 6 | sylibr 133 | . . . . . . . 8 |
8 | dfnul2 3365 | . . . . . . . 8 | |
9 | 7, 8 | sseqtrrdi 3146 | . . . . . . 7 |
10 | 3, 9 | sylbir 134 | . . . . . 6 |
11 | 10 | unissd 3760 | . . . . 5 |
12 | uni0 3763 | . . . . 5 | |
13 | 11, 12 | sseqtrdi 3145 | . . . 4 |
14 | 2, 13 | eqsstrid 3143 | . . 3 |
15 | 1, 14 | sylnbi 667 | . 2 |
16 | ss0 3403 | . 2 | |
17 | 15, 16 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wal 1329 wceq 1331 wex 1468 weu 1999 cab 2125 wss 3071 c0 3363 cuni 3736 cio 5086 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-dif 3073 df-in 3077 df-ss 3084 df-nul 3364 df-sn 3533 df-uni 3737 df-iota 5088 |
This theorem is referenced by: tz6.12-2 5412 0fv 5456 riotaund 5764 |
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