Users' Mathboxes Mathbox for Anthony Hart < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  unqsym1 Structured version   Unicode version

Theorem unqsym1 26176
Description: A symmetry with  E!.

See negsym1 26168 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
StepHypRef Expression
1 unnf 26158 . . . 4  |-  -.  E! x  F.
21nex 1565 . . 3  |-  -.  E. x E! x  F.
3 euex 2305 . . 3  |-  ( E! x E! x  F.  ->  E. x E! x  F.  )
42, 3mto 170 . 2  |-  -.  E! x E! x  F.
54pm2.21i 126 1  |-  ( E! x E! x  F.  ->  E! x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    F. wfal 1327   E.wex 1551   E!weu 2282
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-fal 1330  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2286
  Copyright terms: Public domain W3C validator