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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  |-  -.  A  =/=  A

Proof of Theorem neirr
StepHypRef Expression
1 eqid 2056 . . 3  |-  A  =  A
21notnoti 584 . 2  |-  -.  -.  A  =  A
3 df-ne 2221 . . 3  |-  ( A  =/=  A  <->  -.  A  =  A )
43notbii 604 . 2  |-  ( -.  A  =/=  A  <->  -.  -.  A  =  A )
52, 4mpbir 138 1  |-  -.  A  =/=  A
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  3525  0nnq  6520  1nuz2  8640
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