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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 2422 |
. . 3
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2 | imdistan 441 |
. . . 4
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3 | 2 | albii 1447 |
. . 3
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4 | 1, 3 | bitri 183 |
. 2
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5 | moim 2064 |
. . 3
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6 | df-rmo 2425 |
. . 3
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7 | df-rmo 2425 |
. . 3
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8 | 5, 6, 7 | 3imtr4g 204 |
. 2
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9 | 4, 8 | sylbi 120 |
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 df-ral 2422 df-rmo 2425 |
This theorem is referenced by: rmoimia 2890 disjss2 3917 |
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