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Theorem rmoim 3299
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 2812 . . 3
2 imdistan 689 . . . 4
32albii 1640 . . 3
41, 3bitri 249 . 2
5 moim 2339 . . 3
6 df-rmo 2815 . . 3
7 df-rmo 2815 . . 3
85, 6, 73imtr4g 270 . 2
94, 8sylbi 195 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  e.wcel 1818  E*wmo 2283  A.wral 2807  E*wrmo 2810
This theorem is referenced by:  rmoimia  3300  2rmorex  3304  disjss2  4425  catideu  15072  evlseu  18185  frlmup4  18835  2ndcdisj  19957  reuimrmo  32183  2reurex  32186
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287  df-ral 2812  df-rmo 2815
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