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Theorem rmoi 3431
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:   ,   ,   ,   ,   ,

Proof of Theorem rmoi
StepHypRef Expression
1 rmoi.b . . 3
2 rmoi.c . . 3
31, 2rmob 3430 . 2
43biimp3ar 1329 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  =wceq 1395  e.wcel 1818  E*wrmo 2810
This theorem is referenced by:  eqsqrtd  13200  efgred2  16771  0frgp  16797  frgpnabllem2  16878  frgpcyg  18612  proot1mul  31156  cdleme0moN  35950
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-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rmo 2815  df-v 3111
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