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Theorem ax-9 1440
Description: Derive ax-9 1440 from ax-i9 1439, the modified version for intuitionistic logic. Although ax-9 1440 does hold intuistionistically, in intuitionistic logic it is weaker than ax-i9 1439. (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 1439 . . 3  |-  E. x  x  =  y
21notnoti 584 . 2  |-  -.  -.  E. x  x  =  y
3 alnex 1404 . 2  |-  ( A. x  -.  x  =  y  <->  -.  E. x  x  =  y )
42, 3mtbir 606 1  |-  -.  A. x  -.  x  =  y
Colors of variables: wff set class
Syntax hints:   -. wn 3   A.wal 1257    = wceq 1259   E.wex 1397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-5 1352  ax-gen 1354  ax-ie2 1399  ax-i9 1439
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265
This theorem is referenced by:  equidqe  1441
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