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

Theorem nextf 29798
Description: There does not exist a set, such that F. is true. (Contributed by Anthony Hart, 13-Sep-2011.)
Assertion
Ref Expression
nextf  |-  -.  E. x F.

Proof of Theorem nextf
StepHypRef Expression
1 fal 1386 . 2  |-  -. F.
21nex 1610 1  |-  -.  E. x F.
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   F. wfal 1384   E.wex 1596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601
This theorem depends on definitions:  df-bi 185  df-tru 1382  df-fal 1385  df-ex 1597
This theorem is referenced by:  unnf  29799  mof  29802
  Copyright terms: Public domain W3C validator