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.

Step	Hyp	Ref	Expression
1		dtru 4643	. . . . 5
2		alim 1632	. . . . 5
3	1, 2	mtoi 178	. . . 4
4	3	exlimiv 1722	. . 3
5	4	adantl 466	. 2
6		eu3v 2312	. 2
7		exnal 1648	. 2
8	5, 6, 7	3imtr4i 266	1

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