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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 2700 | . . . . 5 | |
2 | nfcv 2282 | . . . . . . . 8 | |
3 | nfv 1509 | . . . . . . . . . 10 | |
4 | nfmo1 2012 | . . . . . . . . . 10 | |
5 | nfv 1509 | . . . . . . . . . 10 | |
6 | 3, 4, 5 | nf3an 1546 | . . . . . . . . 9 |
7 | nfv 1509 | . . . . . . . . 9 | |
8 | 6, 7 | nfim 1552 | . . . . . . . 8 |
9 | moi.1 | . . . . . . . . . 10 | |
10 | 9 | 3anbi3d 1297 | . . . . . . . . 9 |
11 | eqeq1 2147 | . . . . . . . . . 10 | |
12 | 11 | bibi1d 232 | . . . . . . . . 9 |
13 | 10, 12 | imbi12d 233 | . . . . . . . 8 |
14 | moi.2 | . . . . . . . . 9 | |
15 | 14 | mob2 2868 | . . . . . . . 8 |
16 | 2, 8, 13, 15 | vtoclgf 2747 | . . . . . . 7 |
17 | 16 | com12 30 | . . . . . 6 |
18 | 17 | 3expib 1185 | . . . . 5 |
19 | 1, 18 | syl 14 | . . . 4 |
20 | 19 | com3r 79 | . . 3 |
21 | 20 | imp 123 | . 2 |
22 | 21 | 3impib 1180 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 963 wceq 1332 wcel 1481 wmo 2001 cvv 2689 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 |
This theorem is referenced by: moi 2871 rmob 3005 |
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