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Theorem rmoim 3249
 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 2759 . . 3
2 imdistan 687 . . . 4
32albii 1661 . . 3
41, 3bitri 249 . 2
5 moim 2291 . . 3
6 df-rmo 2762 . . 3
7 df-rmo 2762 . . 3
85, 6, 73imtr4g 270 . 2
94, 8sylbi 195 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 367  wal 1403   wcel 1842  wmo 2239  wral 2754  wrmo 2757 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-12 1878 This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1634  df-nf 1638  df-eu 2242  df-mo 2243  df-ral 2759  df-rmo 2762 This theorem is referenced by:  rmoimia  3250  2rmorex  3254  disjss2  4369  catideu  15289  evlseu  18505  frlmup4  19128  2ndcdisj  20249  reuimrmo  37551  2reurex  37554
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