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Mirrors > Home > ILE Home > Th. List > neirr | Unicode version |
Description: No class is unequal to itself. (Contributed by Stefan O'Rear, 1-Jan-2015.) (Proof rewritten by Jim Kingdon, 15-May-2018.) |
Ref | Expression |
---|---|
neirr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2115 |
. . 3
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2 | 1 | notnoti 617 |
. 2
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3 | df-ne 2283 |
. . 3
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4 | 3 | notbii 640 |
. 2
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5 | 2, 4 | mpbir 145 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 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 2283 |
This theorem is referenced by: neldifsn 3619 0nnq 7120 1nuz2 9302 |
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