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Mirrors > Home > ILE Home > Th. List > mob | Unicode version |
Description: Equality implied by "at most one". (Contributed by NM, 18-Feb-2006.) |
Ref | Expression |
---|---|
moi.1 | |
moi.2 |
Ref | Expression |
---|---|
mob |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2741 | . . . . 5 | |
2 | nfcv 2312 | . . . . . . . 8 | |
3 | nfv 1521 | . . . . . . . . . 10 | |
4 | nfmo1 2031 | . . . . . . . . . 10 | |
5 | nfv 1521 | . . . . . . . . . 10 | |
6 | 3, 4, 5 | nf3an 1559 | . . . . . . . . 9 |
7 | nfv 1521 | . . . . . . . . 9 | |
8 | 6, 7 | nfim 1565 | . . . . . . . 8 |
9 | moi.1 | . . . . . . . . . 10 | |
10 | 9 | 3anbi3d 1313 | . . . . . . . . 9 |
11 | eqeq1 2177 | . . . . . . . . . 10 | |
12 | 11 | bibi1d 232 | . . . . . . . . 9 |
13 | 10, 12 | imbi12d 233 | . . . . . . . 8 |
14 | moi.2 | . . . . . . . . 9 | |
15 | 14 | mob2 2910 | . . . . . . . 8 |
16 | 2, 8, 13, 15 | vtoclgf 2788 | . . . . . . 7 |
17 | 16 | com12 30 | . . . . . 6 |
18 | 17 | 3expib 1201 | . . . . 5 |
19 | 1, 18 | syl 14 | . . . 4 |
20 | 19 | com3r 79 | . . 3 |
21 | 20 | imp 123 | . 2 |
22 | 21 | 3impib 1196 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 973 wceq 1348 wmo 2020 wcel 2141 cvv 2730 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 |
This theorem is referenced by: moi 2913 rmob 3047 |
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