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Mirrors > Home > ILE Home > Th. List > mob2 | Unicode version |
Description: Consequence of "at most one." (Contributed by NM, 2-Jan-2015.) |
Ref | Expression |
---|---|
moi2.1 |
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Ref | Expression |
---|---|
mob2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp3 984 |
. . 3
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2 | moi2.1 |
. . 3
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3 | 1, 2 | syl5ibcom 154 |
. 2
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4 | nfs1v 1913 |
. . . . . . . 8
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5 | sbequ12 1745 |
. . . . . . . 8
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6 | 4, 5 | mo4f 2060 |
. . . . . . 7
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7 | sp 1489 |
. . . . . . 7
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8 | 6, 7 | sylbi 120 |
. . . . . 6
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9 | nfv 1509 |
. . . . . . . . . 10
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10 | 9, 2 | sbhypf 2738 |
. . . . . . . . 9
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11 | 10 | anbi2d 460 |
. . . . . . . 8
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12 | eqeq2 2150 |
. . . . . . . 8
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13 | 11, 12 | imbi12d 233 |
. . . . . . 7
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14 | 13 | spcgv 2776 |
. . . . . 6
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15 | 8, 14 | syl5 32 |
. . . . 5
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16 | 15 | imp 123 |
. . . 4
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17 | 16 | expd 256 |
. . 3
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18 | 17 | 3impia 1179 |
. 2
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19 | 3, 18 | impbid 128 |
1
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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 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: moi2 2869 mob 2870 |
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