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Theorem neirr 2229
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 2056 . . 3 𝐴 = 𝐴
21notnoti 584 . 2 ¬ ¬ 𝐴 = 𝐴
3 df-ne 2221 . . 3 (𝐴𝐴 ↔ ¬ 𝐴 = 𝐴)
43notbii 604 . 2 𝐴𝐴 ↔ ¬ ¬ 𝐴 = 𝐴)
52, 4mpbir 138 1 ¬ 𝐴𝐴
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   = wceq 1259  wne 2220
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-gen 1354  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-ne 2221
This theorem is referenced by:  neldifsn  3524  0nnq  6519  1nuz2  8639
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