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Theorem eunex 4645
Description: Existential uniqueness implies there is a value for which the wff argument is false. (Contributed by NM, 24-Oct-2010.)
Assertion
Ref Expression
eunex

Proof of Theorem eunex
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dtru 4643 . . . . 5
2 alim 1632 . . . . 5
31, 2mtoi 178 . . . 4
43exlimiv 1722 . . 3
54adantl 466 . 2
6 eu3v 2312 . 2
7 exnal 1648 . 2
85, 6, 73imtr4i 266 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612  E!weu 2282
This theorem is referenced by:  reusv2lem2  4654  unnt  29873  amosym1  29891  alneu  32206
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-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-nul 4581  ax-pow 4630
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287
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