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Theorem neirr 2210
Description: No class is unequal to itself. (Contributed by Stefan O'Rear, 1-Jan-2015.) (Proof rewritten by Jim Kingdon, 15-May-2018.)
Assertion
Ref Expression
neirr ¬ AA

Proof of Theorem neirr
StepHypRef Expression
1 eqid 2037 . . 3 A = A
21notnoti 573 . 2 ¬ ¬ A = A
3 df-ne 2203 . . 3 (AA ↔ ¬ A = A)
43notbii 593 . 2 AA ↔ ¬ ¬ A = A)
52, 4mpbir 134 1 ¬ AA
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   = wceq 1242  wne 2201
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-gen 1335  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-ne 2203
This theorem is referenced by:  neldifsn  3488  0nnq  6348  1nuz2  8279
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