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Theorem ax-9 1512
Description: Derive ax-9 1512 from ax-i9 1511, the modified version for intuitionistic logic. Although ax-9 1512 does hold intuistionistically, in intuitionistic logic it is weaker than ax-i9 1511. (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 1511 . . 3  |-  E. x  x  =  y
21notnoti 635 . 2  |-  -.  -.  E. x  x  =  y
3 alnex 1476 . 2  |-  ( A. x  -.  x  =  y  <->  -.  E. x  x  =  y )
42, 3mtbir 661 1  |-  -.  A. x  -.  x  =  y
Colors of variables: wff set class
Syntax hints:   -. wn 3   A.wal 1330    = wceq 1332   E.wex 1469
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 604  ax-in2 605  ax-5 1424  ax-gen 1426  ax-ie2 1471  ax-i9 1511
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338
This theorem is referenced by:  equidqe  1513
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