Metamath Proof Explorer
Description: Two classes are not equal if one but not the other is an element of a
given class. (Contributed by Rohan Ridenour, 12-Aug-2023)
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|
Ref |
Expression |
|
Hypotheses |
elnelneq2d.1 |
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|
|
elnelneq2d.2 |
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Assertion |
elnelneq2d |
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Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
elnelneq2d.1 |
|
2 |
|
elnelneq2d.2 |
|
3 |
|
simpr |
|
4 |
1
|
adantr |
|
5 |
3 4
|
eqeltrrd |
|
6 |
2 5
|
mtand |
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