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Mirrors > Home > ILE Home > Th. List > moim | Unicode version |
Description: "At most one" is preserved through implication (notice wff reversal). (Contributed by NM, 22-Apr-1995.) |
Ref | Expression |
---|---|
moim |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1522 |
. . 3
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2 | ax-4 1488 |
. . . . . 6
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3 | spsbim 1816 |
. . . . . 6
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4 | 2, 3 | anim12d 333 |
. . . . 5
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5 | 4 | imim1d 75 |
. . . 4
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6 | 5 | alimdv 1852 |
. . 3
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7 | 1, 6 | alimd 1502 |
. 2
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8 | ax-17 1507 |
. . 3
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9 | 8 | mo3h 2053 |
. 2
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10 | ax-17 1507 |
. . 3
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11 | 10 | mo3h 2053 |
. 2
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12 | 7, 9, 11 | 3imtr4g 204 |
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 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 |
This theorem is referenced by: moimi 2065 euimmo 2067 moexexdc 2084 euexex 2085 rmoim 2889 rmoimi2 2891 ssrmof 3165 disjss1 3920 reusv1 4387 funmo 5146 uptx 12482 |
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