ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax-9 Unicode version

Theorem ax-9 1469
Description: Derive ax-9 1469 from ax-i9 1468, the modified version for intuitionistic logic. Although ax-9 1469 does hold intuistionistically, in intuitionistic logic it is weaker than ax-i9 1468. (Contributed by NM, 3-Feb-2015.)
Assertion
Ref Expression
ax-9  |-  -.  A. x  -.  x  =  y

Proof of Theorem ax-9
StepHypRef Expression
1 ax-i9 1468 . . 3  |-  E. x  x  =  y
21notnoti 609 . 2  |-  -.  -.  E. x  x  =  y
3 alnex 1433 . 2  |-  ( A. x  -.  x  =  y  <->  -.  E. x  x  =  y )
42, 3mtbir 631 1  |-  -.  A. x  -.  x  =  y
Colors of variables: wff set class
Syntax hints:   -. wn 3   A.wal 1287    = wceq 1289   E.wex 1426
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-5 1381  ax-gen 1383  ax-ie2 1428  ax-i9 1468
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295
This theorem is referenced by:  equidqe  1470
  Copyright terms: Public domain W3C validator