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Mirrors > Home > ILE Home > Th. List > mo2n | Unicode version |
Description: There is at most one of something which does not exist. (Contributed by Jim Kingdon, 2-Jul-2018.) |
Ref | Expression |
---|---|
mon.1 |
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Ref | Expression |
---|---|
mo2n |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mon.1 |
. . 3
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2 | 1 | sb8e 1868 |
. 2
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3 | alnex 1510 |
. . 3
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4 | nfs1v 1951 |
. . . . . 6
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5 | 4 | nfn 1669 |
. . . . 5
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6 | 1 | nfn 1669 |
. . . . 5
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7 | sbequ1 1779 |
. . . . . . 7
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8 | 7 | equcoms 1719 |
. . . . . 6
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9 | 8 | con3d 632 |
. . . . 5
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10 | 5, 6, 9 | cbv3 1753 |
. . . 4
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11 | pm2.21 618 |
. . . . 5
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12 | 11 | alimi 1466 |
. . . 4
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13 | 19.8a 1601 |
. . . 4
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14 | 10, 12, 13 | 3syl 17 |
. . 3
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15 | 3, 14 | sylbir 135 |
. 2
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16 | 2, 15 | sylnbi 679 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 |
This theorem is referenced by: modc 2081 |
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