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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 2440 | . . 3 | |
2 | imdistan 441 | . . . 4 | |
3 | 2 | albii 1450 | . . 3 |
4 | 1, 3 | bitri 183 | . 2 |
5 | moim 2070 | . . 3 | |
6 | df-rmo 2443 | . . 3 | |
7 | df-rmo 2443 | . . 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 1333 wmo 2007 wcel 2128 wral 2435 wrmo 2438 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-ral 2440 df-rmo 2443 |
This theorem is referenced by: rmoimia 2914 disjss2 3945 |
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