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Theorem moi 3019
 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 3018 . . . . 5
43biimprd 214 . . . 4
543expia 1153 . . 3
65imp3a 420 . 2
763impia 1148 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   w3a 934   wceq 1642   wcel 1710  wmo 2205 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861 This theorem is referenced by: (None)
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