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Theorem rmoim 3035
 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 2619 . . 3
2 imdistan 670 . . . 4
32albii 1566 . . 3
41, 3bitri 240 . 2
5 moim 2250 . . 3
6 df-rmo 2622 . . 3
7 df-rmo 2622 . . 3
85, 6, 73imtr4g 261 . 2
94, 8sylbi 187 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358  wal 1540   wcel 1710  wmo 2205  wral 2614  wrmo 2617 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-ral 2619  df-rmo 2622 This theorem is referenced by:  rmoimia  3036  2rmorex  3040
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