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Mirrors > Home > ILE Home > Th. List > rmoim | Unicode version |
Description: Restricted "at most one" is preserved through implication (note wff reversal). (Contributed by Alexander van der Vekens, 17-Jun-2017.) |
Ref | Expression |
---|---|
rmoim |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2305 |
. . 3
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2 | imdistan 418 |
. . . 4
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3 | 2 | albii 1356 |
. . 3
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4 | 1, 3 | bitri 173 |
. 2
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5 | moim 1961 |
. . 3
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6 | df-rmo 2308 |
. . 3
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7 | df-rmo 2308 |
. . 3
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8 | 5, 6, 7 | 3imtr4g 194 |
. 2
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9 | 4, 8 | sylbi 114 |
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 df-ral 2305 df-rmo 2308 |
This theorem is referenced by: rmoimia 2735 disjss2 3739 |
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