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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 2631 |
. . . . 5
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2 | nfcv 2229 |
. . . . . . . 8
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3 | nfv 1467 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() | |
4 | nfmo1 1961 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() | |
5 | nfv 1467 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() | |
6 | 3, 4, 5 | nf3an 1504 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | nfv 1467 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 6, 7 | nfim 1510 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | moi.1 |
. . . . . . . . . 10
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10 | 9 | 3anbi3d 1255 |
. . . . . . . . 9
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11 | eqeq1 2095 |
. . . . . . . . . 10
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12 | 11 | bibi1d 232 |
. . . . . . . . 9
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13 | 10, 12 | imbi12d 233 |
. . . . . . . 8
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14 | moi.2 |
. . . . . . . . 9
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15 | 14 | mob2 2796 |
. . . . . . . 8
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16 | 2, 8, 13, 15 | vtoclgf 2678 |
. . . . . . 7
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17 | 16 | com12 30 |
. . . . . 6
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18 | 17 | 3expib 1147 |
. . . . 5
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19 | 1, 18 | syl 14 |
. . . 4
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20 | 19 | com3r 79 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | 20 | imp 123 |
. 2
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22 | 21 | 3impib 1142 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-v 2622 |
This theorem is referenced by: moi 2799 rmob 2932 |
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