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Definition df-enr 9454
Description: Define equivalence relation for signed reals. This is a "temporary" set used in the construction of complex numbers df-c 9519, and is intended to be used only by the construction. From Proposition 9-4.1 of [Gleason] p. 126. (Contributed by NM, 25-Jul-1995.) (New usage is discouraged.)
Assertion
Ref Expression
df-enr
Distinct variable group:   , , , , ,

Detailed syntax breakdown of Definition df-enr
StepHypRef Expression
1 cer 9263 . 2
2 vx . . . . . . 7
32cv 1394 . . . . . 6
4 cnp 9258 . . . . . . 7
54, 4cxp 5002 . . . . . 6
63, 5wcel 1818 . . . . 5
7 vy . . . . . . 7
87cv 1394 . . . . . 6
98, 5wcel 1818 . . . . 5
106, 9wa 369 . . . 4
11 vz . . . . . . . . . . . . 13
1211cv 1394 . . . . . . . . . . . 12
13 vw . . . . . . . . . . . . 13
1413cv 1394 . . . . . . . . . . . 12
1512, 14cop 4035 . . . . . . . . . . 11
163, 15wceq 1395 . . . . . . . . . 10
17 vv . . . . . . . . . . . . 13
1817cv 1394 . . . . . . . . . . . 12
19 vu . . . . . . . . . . . . 13
2019cv 1394 . . . . . . . . . . . 12
2118, 20cop 4035 . . . . . . . . . . 11
228, 21wceq 1395 . . . . . . . . . 10
2316, 22wa 369 . . . . . . . . 9
24 cpp 9260 . . . . . . . . . . 11
2512, 20, 24co 6296 . . . . . . . . . 10
2614, 18, 24co 6296 . . . . . . . . . 10
2725, 26wceq 1395 . . . . . . . . 9
2823, 27wa 369 . . . . . . . 8
2928, 19wex 1612 . . . . . . 7
3029, 17wex 1612 . . . . . 6
3130, 13wex 1612 . . . . 5
3231, 11wex 1612 . . . 4
3310, 32wa 369 . . 3
3433, 2, 7copab 4509 . 2
351, 34wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  enrbreq  9462  enrer  9463  enrex  9465  prsrlem1  9470
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