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Theorem rmo4 3127
 Description: Restricted "at most one" using implicit substitution. (Contributed by NM, 24-Oct-2006.) (Revised by NM, 16-Jun-2017.)
Hypothesis
Ref Expression
rmo4.1
Assertion
Ref Expression
rmo4
Distinct variable groups:   ,,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rmo4
StepHypRef Expression
1 df-rmo 2713 . 2
2 an4 798 . . . . . . . . 9
3 ancom 438 . . . . . . . . . 10
43anbi1i 677 . . . . . . . . 9
52, 4bitri 241 . . . . . . . 8
65imbi1i 316 . . . . . . 7
7 impexp 434 . . . . . . 7
8 impexp 434 . . . . . . 7
96, 7, 83bitri 263 . . . . . 6
109albii 1575 . . . . 5
11 df-ral 2710 . . . . 5
12 r19.21v 2793 . . . . 5
1310, 11, 123bitr2i 265 . . . 4
1413albii 1575 . . 3
15 eleq1 2496 . . . . 5
16 rmo4.1 . . . . 5
1715, 16anbi12d 692 . . . 4
1817mo4 2314 . . 3
19 df-ral 2710 . . 3
2014, 18, 193bitr4i 269 . 2
211, 20bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wcel 1725  wmo 2282  wral 2705  wrmo 2708 This theorem is referenced by:  reu4  3128  disjor  4196  somo  4537  supmo  7457  sqrmo  12057  catideu  13900  poslubmo  14573  mgmidmo  14693  lspextmo  16132  evlseu  19937  ply1divmo  20058  cvmliftmo  24971  hilbert1.2  26089  idomsubgmo  27491 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-cleq 2429  df-clel 2432  df-ral 2710  df-rmo 2713
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