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Definition df-er 7185
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 7186 we derive a more typical definition. We show that an equivalence relation is reflexive, symmetric, and transitive in erref 7205, ersymb 7199, and ertr 7200. (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 7182 . 2
42wrel 4927 . . 3
52cdm 4922 . . . 4
65, 1wceq 1370 . . 3
72ccnv 4921 . . . . 5
82, 2ccom 4926 . . . . 5
97, 8cun 3408 . . . 4
109, 2wss 3410 . . 3
114, 6, 10w3a 965 . 2
123, 11wb 184 1
Colors of variables: wff setvar class
This definition is referenced by:  dfer2  7186  ereq1  7192  ereq2  7193  errel  7194  erdm  7195  ersym  7197  ertr  7200  xpider  7255
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