Theorem unqsym1 32424

Description: A symmetry with E!.

See negsym1 32416 for more information. (Contributed by Anthony Hart, 6-Sep-2011.)

Assertion

Ref	Expression
unqsym1	|- ( E! x E! x F. -> E! x ph )

Proof of Theorem unqsym1

Step	Hyp	Ref	Expression
1		unnf 32406	. . . 4 |- -. E! x F.
2	1	nex 1731	. . 3 |- -. E. x E! x F.
3		euex 2494	. . 3 |- ( E! x E! x F. -> E. x E! x F. )
4	2, 3	mto 188	. 2 |- -. E! x E! x F.
5	4	pm2.21i 116	1 |- ( E! x E! x F. -> E! x ph )

Syntax hints:   -> wi 4   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: (None)