ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  alexnim Unicode version

Theorem alexnim 1627
Description: A relationship between two quantifiers and negation. (Contributed by Jim Kingdon, 27-Aug-2018.)
Assertion
Ref Expression
alexnim  |-  ( A. x E. y  -.  ph  ->  -.  E. x A. y ph )

Proof of Theorem alexnim
StepHypRef Expression
1 exnalim 1625 . . 3  |-  ( E. y  -.  ph  ->  -. 
A. y ph )
21alimi 1431 . 2  |-  ( A. x E. y  -.  ph  ->  A. x  -.  A. y ph )
3 alnex 1475 . 2  |-  ( A. x  -.  A. y ph  <->  -. 
E. x A. y ph )
42, 3sylib 121 1  |-  ( A. x E. y  -.  ph  ->  -.  E. x A. y ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1329   E.wex 1468
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437
This theorem is referenced by:  nalset  4053  bj-nalset  13082
  Copyright terms: Public domain W3C validator