Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  rmoi2 Structured version   Unicode version

Theorem rmoi2 3374
 Description: Consequence of "restricted at most one." (Contributed by Thierry Arnoux, 9-Dec-2019.)
Hypotheses
Ref Expression
rmoi2.1
rmoi2.2
rmoi2.3
rmoi2.4
rmoi2.5
rmoi2.6
Assertion
Ref Expression
rmoi2
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rmoi2
StepHypRef Expression
1 rmoi2.6 . 2
2 rmoi2.1 . . 3
3 rmoi2.2 . . 3
4 rmoi2.3 . . 3
5 rmoi2.4 . . 3
6 rmoi2.5 . . 3
72, 3, 4, 5, 6rmob2 3373 . 2
81, 7mpbird 234 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 186   wceq 1407   wcel 1844  wrmo 2759 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382 This theorem depends on definitions:  df-bi 187  df-or 370  df-an 371  df-3an 978  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-eu 2244  df-mo 2245  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-rmo 2764  df-v 3063 This theorem is referenced by:  lmieu  24545
 Copyright terms: Public domain W3C validator