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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 905 |
. . 3
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2 | moi2.1 |
. . 3
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3 | 1, 2 | syl5ibcom 144 |
. 2
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4 | nfs1v 1812 |
. . . . . . . 8
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5 | sbequ12 1651 |
. . . . . . . 8
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6 | 4, 5 | mo4f 1957 |
. . . . . . 7
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7 | sp 1398 |
. . . . . . 7
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8 | 6, 7 | sylbi 114 |
. . . . . 6
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9 | nfv 1418 |
. . . . . . . . . 10
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10 | 9, 2 | sbhypf 2597 |
. . . . . . . . 9
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11 | 10 | anbi2d 437 |
. . . . . . . 8
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12 | eqeq2 2046 |
. . . . . . . 8
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13 | 11, 12 | imbi12d 223 |
. . . . . . 7
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14 | 13 | spcgv 2634 |
. . . . . 6
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15 | 8, 14 | syl5 28 |
. . . . 5
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16 | 15 | imp 115 |
. . . 4
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17 | 16 | expd 245 |
. . 3
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18 | 17 | 3impia 1100 |
. 2
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19 | 3, 18 | impbid 120 |
1
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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 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 |
This theorem is referenced by: moi2 2716 mob 2717 |
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