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Theorem ax-9 1300
 Description: Derive ax-9 1300 from ax-i9 1299, the modified version for intuitionistic logic. Although ax-9 1300 does hold intuistionistically, in intuitionistic logic it is weaker than ax-i9 1299. (Contributed by NM, 3-Feb-2015.)
Assertion
Ref Expression
ax-9 ¬ x ¬ x = y

Proof of Theorem ax-9
StepHypRef Expression
1 ax-i9 1299 . . 3 x x = y
21notnoti 552 . 2 ¬ ¬ x x = y
3 alnex 1276 . 2 (x ¬ x = y ↔ ¬ x x = y)
42, 3mtbir 574 1 ¬ x ¬ x = y
 Colors of variables: wff set class Syntax hints:  ¬ wn 3  ∀wal 1231  ∃wex 1270   = wceq 1279 This theorem is referenced by:  equidqe  1301  equidqeOLD  1302  ax4  1809 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8  ax-ia1 98  ax-ia2 99  ax-ia3 100  ax-in1 526  ax-in2 527  ax-5 1232  ax-gen 1235  ax-ie2 1272  ax-i9 1299 This theorem depends on definitions:  df-bi 109  df-tru 1209  df-fal 1210
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