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Theorem rmoi 3382
 Description: Consequence of "at most one", using implicit substitution. (Contributed by NM, 4-Nov-2012.) (Revised by NM, 16-Jun-2017.)
Hypotheses
Ref Expression
rmoi.b
rmoi.c
Assertion
Ref Expression
rmoi
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rmoi
StepHypRef Expression
1 rmoi.b . . 3
2 rmoi.c . . 3
31, 2rmob 3381 . 2
43biimp3ar 1320 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 965   wceq 1370   wcel 1758  wrmo 2796 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2264  df-mo 2265  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2599  df-rmo 2801  df-v 3067 This theorem is referenced by:  eqsqrd  12954  efgred2  16351  0frgp  16377  frgpnabllem2  16453  frgpcyg  18112  qtophmeo  19503  proot1mul  29699  cdleme0moN  34172
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