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Theorem ax-9 1421
 Description: Derive ax-9 1421 from ax-i9 1420, the modified version for intuitionistic logic. Although ax-9 1421 does hold intuistionistically, in intuitionistic logic it is weaker than ax-i9 1420. (Contributed by NM, 3-Feb-2015.)
Assertion
Ref Expression
ax-9 ¬ x ¬ x = y

Proof of Theorem ax-9
StepHypRef Expression
1 ax-i9 1420 . . 3 x x = y
21notnoti 573 . 2 ¬ ¬ x x = y
3 alnex 1385 . 2 (x ¬ x = y ↔ ¬ x x = y)
42, 3mtbir 595 1 ¬ x ¬ x = y
 Colors of variables: wff set class Syntax hints:  ¬ wn 3  ∀wal 1240   = wceq 1242  ∃wex 1378 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 1333  ax-gen 1335  ax-ie2 1380  ax-i9 1420 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248 This theorem is referenced by:  equidqe  1422
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