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Theorem rmoim 2734
Description: Restricted "at most one" is preserved through implication (note wff reversal). (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Assertion
Ref Expression
rmoim

Proof of Theorem rmoim
StepHypRef Expression
1 df-ral 2305 . . 3
2 imdistan 418 . . . 4
32albii 1356 . . 3
41, 3bitri 173 . 2
5 moim 1961 . . 3
6 df-rmo 2308 . . 3
7 df-rmo 2308 . . 3
85, 6, 73imtr4g 194 . 2
94, 8sylbi 114 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wal 1240   wcel 1390  wmo 1898  wral 2300  wrmo 2303
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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