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

Theorem alexnim 1539
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 1537 . . 3  |-  ( E. y  -.  ph  ->  -. 
A. y ph )
21alimi 1344 . 2  |-  ( A. x E. y  -.  ph  ->  A. x  -.  A. y ph )
3 alnex 1388 . 2  |-  ( A. x  -.  A. y ph  <->  -. 
E. x A. y ph )
42, 3sylib 127 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 1241   E.wex 1381
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350
This theorem is referenced by:  nalset  3887  bj-nalset  9988
  Copyright terms: Public domain W3C validator