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Definition df-er 6905
 Description: Define the equivalence relation predicate. Our notation is not standard. A formal notation doesn't seem to exist in the literature; instead only informal English tends to be used. The present definition, although somewhat cryptic, nicely avoids dummy variables. In dfer2 6906 we derive a more typical definition. We show that an equivalence relation is reflexive, symmetric, and transitive in erref 6925, ersymb 6919, and ertr 6920. (Contributed by NM, 4-Jun-1995.) (Revised by Mario Carneiro, 2-Nov-2015.)
Assertion
Ref Expression
df-er

Detailed syntax breakdown of Definition df-er
StepHypRef Expression
1 cA . . 3
2 cR . . 3
31, 2wer 6902 . 2
42wrel 4883 . . 3
52cdm 4878 . . . 4
65, 1wceq 1652 . . 3
72ccnv 4877 . . . . 5
82, 2ccom 4882 . . . . 5
97, 8cun 3318 . . . 4
109, 2wss 3320 . . 3
114, 6, 10w3a 936 . 2
123, 11wb 177 1
 Colors of variables: wff set class This definition is referenced by:  dfer2  6906  ereq1  6912  ereq2  6913  errel  6914  erdm  6915  ersym  6917  ertr  6920  xpider  6975
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