Theorem unnf 32406

Description: There does not exist exactly one set, such that F. is true. (Contributed by Anthony Hart, 13-Sep-2011.)

Assertion

Ref	Expression
unnf	|- -. E! x F.

Proof of Theorem unnf

Step	Hyp	Ref	Expression
1		nextf 32405	. 2 |- -. E. x F.
2		euex 2494	. 2 |- ( E! x F. -> E. x F. )
3	1, 2	mto 188	1 |- -. E! x F.

Syntax hints:   -. wn 3   F. wfal 1488   E.wex 1704   E!weu 2470

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-tru 1486  df-fal 1489  df-ex 1705  df-eu 2474

This theorem is referenced by:  unqsym1  32424