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Theorem rmoim 3134
 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 2711 . . 3
2 imdistan 672 . . . 4
32albii 1576 . . 3
41, 3bitri 242 . 2
5 moim 2328 . . 3
6 df-rmo 2714 . . 3
7 df-rmo 2714 . . 3
85, 6, 73imtr4g 263 . 2
94, 8sylbi 189 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360  wal 1550   wcel 1726  wmo 2283  wral 2706  wrmo 2709 This theorem is referenced by:  rmoimia  3135  2rmorex  3139  disjss2  4186  catideu  13901  2ndcdisj  17520  evlseu  19938  frlmup4  27231  reuimrmo  27933  2reurex  27936 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2286  df-mo 2287  df-ral 2711  df-rmo 2714
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