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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 2723 | . . . . 5 | |
2 | nfcv 2299 | . . . . . . . 8 | |
3 | nfv 1508 | . . . . . . . . . 10 | |
4 | nfmo1 2018 | . . . . . . . . . 10 | |
5 | nfv 1508 | . . . . . . . . . 10 | |
6 | 3, 4, 5 | nf3an 1546 | . . . . . . . . 9 |
7 | nfv 1508 | . . . . . . . . 9 | |
8 | 6, 7 | nfim 1552 | . . . . . . . 8 |
9 | moi.1 | . . . . . . . . . 10 | |
10 | 9 | 3anbi3d 1300 | . . . . . . . . 9 |
11 | eqeq1 2164 | . . . . . . . . . 10 | |
12 | 11 | bibi1d 232 | . . . . . . . . 9 |
13 | 10, 12 | imbi12d 233 | . . . . . . . 8 |
14 | moi.2 | . . . . . . . . 9 | |
15 | 14 | mob2 2892 | . . . . . . . 8 |
16 | 2, 8, 13, 15 | vtoclgf 2770 | . . . . . . 7 |
17 | 16 | com12 30 | . . . . . 6 |
18 | 17 | 3expib 1188 | . . . . 5 |
19 | 1, 18 | syl 14 | . . . 4 |
20 | 19 | com3r 79 | . . 3 |
21 | 20 | imp 123 | . 2 |
22 | 21 | 3impib 1183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 963 wceq 1335 wmo 2007 wcel 2128 cvv 2712 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 |
This theorem is referenced by: moi 2895 rmob 3029 |
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