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

Theorem moi 3286
 Description: Equality implied by "at most one." (Contributed by NM, 18-Feb-2006.)
Hypotheses
Ref Expression
moi.1
moi.2
Assertion
Ref Expression
moi
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem moi
StepHypRef Expression
1 moi.1 . . . . . 6
2 moi.2 . . . . . 6
31, 2mob 3285 . . . . 5
43biimprd 223 . . . 4
543expia 1198 . . 3
65impd 431 . 2
763impia 1193 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 973   wceq 1379   wcel 1767  wmo 2276 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115 This theorem is referenced by:  enqeq  9312  f1otrspeq  16278  hausflim  20245  tglineineq  23764  tglineinteq  23766
 Copyright terms: Public domain W3C validator