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Theorem 2mos 2362
 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:   ,,   ,,   ,,,
Allowed substitution hints:   (,)   (,)

Proof of Theorem 2mos
StepHypRef Expression
1 2mo 2361 . 2
2 nfv 1630 . . . . . . 7
3 2mos.1 . . . . . . . 8
43sbiedv 2155 . . . . . . 7
52, 4sbie 2151 . . . . . 6
65anbi2i 677 . . . . 5
76imbi1i 317 . . . 4
872albii 1577 . . 3
982albii 1577 . 2
101, 9bitri 242 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wex 1551  wsb 1659 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660
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