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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 1431 |
. . 3
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2 | ax-4 1397 |
. . . . . 6
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3 | spsbim 1721 |
. . . . . 6
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4 | 2, 3 | anim12d 318 |
. . . . 5
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5 | 4 | imim1d 69 |
. . . 4
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6 | 5 | alimdv 1756 |
. . 3
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7 | 1, 6 | alimd 1411 |
. 2
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8 | ax-17 1416 |
. . 3
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9 | 8 | mo3h 1950 |
. 2
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10 | ax-17 1416 |
. . 3
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11 | 10 | mo3h 1950 |
. 2
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12 | 7, 9, 11 | 3imtr4g 194 |
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 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 |
This theorem is referenced by: moimi 1962 euimmo 1964 moexexdc 1981 euexex 1982 rmoim 2734 rmoimi2 2736 disjss1 3742 reusv1 4156 funmo 4860 |
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