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Mirrors > Home > ILE Home > Th. List > sniota | Unicode version |
Description: A class abstraction with a unique member can be expressed as a singleton. (Contributed by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
sniota |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfeu1 2024 | . . 3 | |
2 | iota1 5161 | . . . . 5 | |
3 | eqcom 2166 | . . . . 5 | |
4 | 2, 3 | bitrdi 195 | . . . 4 |
5 | abid 2152 | . . . 4 | |
6 | vex 2724 | . . . . 5 | |
7 | 6 | elsn 3586 | . . . 4 |
8 | 4, 5, 7 | 3bitr4g 222 | . . 3 |
9 | 1, 8 | alrimi 1509 | . 2 |
10 | nfab1 2308 | . . 3 | |
11 | nfiota1 5149 | . . . 4 | |
12 | 11 | nfsn 3630 | . . 3 |
13 | 10, 12 | cleqf 2331 | . 2 |
14 | 9, 13 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1340 wceq 1342 weu 2013 wcel 2135 cab 2150 csn 3570 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-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-nf 1448 df-sb 1750 df-eu 2016 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-rex 2448 df-v 2723 df-sbc 2947 df-un 3115 df-sn 3576 df-pr 3577 df-uni 3784 df-iota 5147 |
This theorem is referenced by: snriota 5821 |
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