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Theorem ax-9 1322
Description: Derive ax-9 1322 from ax-i9 1321, the modified version for intuitionistic logic. Although ax-9 1322 does hold intuistionistically, in intuitionistic logic it is weaker than ax-i9 1321. (Contributed by NM, 3-Feb-2015.)
Assertion
Ref Expression
ax-9 ¬ x ¬ x = y

Proof of Theorem ax-9
StepHypRef Expression
1 ax-i9 1321 . . 3 x x = y
21notnoti 552 . 2 ¬ ¬ x x = y
3 alnex 1298 . 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 1253  wex 1292   = wceq 1301
This theorem is referenced by:  equidqe  1323  equidqeOLD  1324  ax4  1326
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 1254  ax-gen 1257  ax-ie2 1294  ax-i9 1321
This theorem depends on definitions:  df-bi 109  df-tru 1231  df-fal 1232
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