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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 |
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moi.2 |
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Ref | Expression |
---|---|
mob |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2760 |
. . . . 5
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2 | nfcv 2329 |
. . . . . . . 8
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3 | nfv 1538 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() | |
4 | nfmo1 2048 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() | |
5 | nfv 1538 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() | |
6 | 3, 4, 5 | nf3an 1576 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | nfv 1538 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 6, 7 | nfim 1582 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | moi.1 |
. . . . . . . . . 10
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10 | 9 | 3anbi3d 1328 |
. . . . . . . . 9
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11 | eqeq1 2194 |
. . . . . . . . . 10
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12 | 11 | bibi1d 233 |
. . . . . . . . 9
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13 | 10, 12 | imbi12d 234 |
. . . . . . . 8
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14 | moi.2 |
. . . . . . . . 9
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15 | 14 | mob2 2929 |
. . . . . . . 8
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16 | 2, 8, 13, 15 | vtoclgf 2807 |
. . . . . . 7
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17 | 16 | com12 30 |
. . . . . 6
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18 | 17 | 3expib 1207 |
. . . . 5
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19 | 1, 18 | syl 14 |
. . . 4
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20 | 19 | com3r 79 |
. . 3
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21 | 20 | imp 124 |
. 2
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22 | 21 | 3impib 1202 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-v 2751 |
This theorem is referenced by: moi 2932 rmob 3067 2omotaplemst 7271 |
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