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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 2566 | . . . . 5 | |
2 | nfcv 2178 | . . . . . . . 8 | |
3 | nfv 1421 | . . . . . . . . . 10 | |
4 | nfmo1 1912 | . . . . . . . . . 10 | |
5 | nfv 1421 | . . . . . . . . . 10 | |
6 | 3, 4, 5 | nf3an 1458 | . . . . . . . . 9 |
7 | nfv 1421 | . . . . . . . . 9 | |
8 | 6, 7 | nfim 1464 | . . . . . . . 8 |
9 | moi.1 | . . . . . . . . . 10 | |
10 | 9 | 3anbi3d 1213 | . . . . . . . . 9 |
11 | eqeq1 2046 | . . . . . . . . . 10 | |
12 | 11 | bibi1d 222 | . . . . . . . . 9 |
13 | 10, 12 | imbi12d 223 | . . . . . . . 8 |
14 | moi.2 | . . . . . . . . 9 | |
15 | 14 | mob2 2721 | . . . . . . . 8 |
16 | 2, 8, 13, 15 | vtoclgf 2612 | . . . . . . 7 |
17 | 16 | com12 27 | . . . . . 6 |
18 | 17 | 3expib 1107 | . . . . 5 |
19 | 1, 18 | syl 14 | . . . 4 |
20 | 19 | com3r 73 | . . 3 |
21 | 20 | imp 115 | . 2 |
22 | 21 | 3impib 1102 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 wceq 1243 wcel 1393 wmo 1901 cvv 2557 |
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-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-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 |
This theorem is referenced by: moi 2724 rmob 2850 |
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