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Definition df-er 7330
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 7331 we derive a more typical definition. We show that an equivalence relation is reflexive, symmetric, and transitive in erref 7350, ersymb 7344, and ertr 7345. (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 7327 . 2
42wrel 5009 . . 3
52cdm 5004 . . . 4
65, 1wceq 1395 . . 3
72ccnv 5003 . . . . 5
82, 2ccom 5008 . . . . 5
97, 8cun 3473 . . . 4
109, 2wss 3475 . . 3
114, 6, 10w3a 973 . 2
123, 11wb 184 1
Colors of variables: wff setvar class
This definition is referenced by:  dfer2  7331  ereq1  7337  ereq2  7338  errel  7339  erdm  7340  ersym  7342  ertr  7345  xpider  7401  fcoinver  27460
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