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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2453 | . . 3 | |
2 | imdistan 442 | . . . 4 | |
3 | 2 | albii 1463 | . . 3 |
4 | 1, 3 | bitri 183 | . 2 |
5 | moim 2083 | . . 3 | |
6 | df-rmo 2456 | . . 3 | |
7 | df-rmo 2456 | . . 3 | |
8 | 5, 6, 7 | 3imtr4g 204 | . 2 |
9 | 4, 8 | sylbi 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1346 wmo 2020 wcel 2141 wral 2448 wrmo 2451 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-ral 2453 df-rmo 2456 |
This theorem is referenced by: rmoimia 2932 disjss2 3969 |
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