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Theorem rmoim 2763
 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 2328 . . 3
2 imdistan 426 . . . 4
32albii 1375 . . 3
41, 3bitri 177 . 2
5 moim 1980 . . 3
6 df-rmo 2331 . . 3
7 df-rmo 2331 . . 3
85, 6, 73imtr4g 198 . 2
94, 8sylbi 118 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101  wal 1257   wcel 1409  wmo 1917  wral 2323  wrmo 2326 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920  df-ral 2328  df-rmo 2331 This theorem is referenced by:  rmoimia  2764  disjss2  3776
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