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Theorem moi 2873
 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 2872 . . . . 5
43biimprd 157 . . . 4
543expia 1184 . . 3
65impd 252 . 2
763impia 1179 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   w3a 963   wceq 1332  wmo 1991   wcel 2112 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1732  df-eu 1993  df-mo 1994  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-v 2693 This theorem is referenced by: (None)
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