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Theorem neirr 2292
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 2115 . . 3 𝐴 = 𝐴
21notnoti 617 . 2 ¬ ¬ 𝐴 = 𝐴
3 df-ne 2284 . . 3 (𝐴𝐴 ↔ ¬ 𝐴 = 𝐴)
43notbii 640 . 2 𝐴𝐴 ↔ ¬ ¬ 𝐴 = 𝐴)
52, 4mpbir 145 1 ¬ 𝐴𝐴
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   = wceq 1314  wne 2283
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-gen 1408  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-cleq 2108  df-ne 2284
This theorem is referenced by:  neldifsn  3621  0nnq  7136  1nuz2  9349
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