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Theorem 2mos 2375
 Description: Double "exists at most one", using implicit substitution. (Contributed by NM, 10-Feb-2005.)
Hypothesis
Ref Expression
2mos.1
Assertion
Ref Expression
2mos
Distinct variable groups:   ,,   ,,   ,,,

Proof of Theorem 2mos
StepHypRef Expression
1 2mo 2373 . 2
2 nfv 1707 . . . . . . 7
3 2mos.1 . . . . . . . 8
43sbiedv 2152 . . . . . . 7
52, 4sbie 2149 . . . . . 6
65anbi2i 694 . . . . 5
76imbi1i 325 . . . 4
872albii 1641 . . 3
982albii 1641 . 2
101, 9bitri 249 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  [wsb 1739 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 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287
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