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Definition df-enr 6654
Description: Define equivalence relation for signed reals. This is a "temporary" set used in the construction of complex numbers, 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.)
Assertion
Ref Expression
df-enr  ~R  { <. , 
>.  |  P.  X.  P.  P.  X.  P. 
<. ,  >.  <. ,  >.  +P.  +P.  }
Distinct variable group:   ,,,,,

Detailed syntax breakdown of Definition df-enr
StepHypRef Expression
1 cer 6280 . 2  ~R
2 vx . . . . . . 7  setvar
32cv 1241 . . . . . 6
4 cnp 6275 . . . . . . 7  P.
54, 4cxp 4286 . . . . . 6  P. 
X.  P.
63, 5wcel 1390 . . . . 5  P.  X.  P.
7 vy . . . . . . 7  setvar
87cv 1241 . . . . . 6
98, 5wcel 1390 . . . . 5  P.  X.  P.
106, 9wa 97 . . . 4  P.  X.  P.  P.  X.  P.
11 vz . . . . . . . . . . . . 13  setvar
1211cv 1241 . . . . . . . . . . . 12
13 vw . . . . . . . . . . . . 13  setvar
1413cv 1241 . . . . . . . . . . . 12
1512, 14cop 3370 . . . . . . . . . . 11  <. ,  >.
163, 15wceq 1242 . . . . . . . . . 10  <. ,  >.
17 vv . . . . . . . . . . . . 13  setvar
1817cv 1241 . . . . . . . . . . . 12
19 vu . . . . . . . . . . . . 13  setvar
2019cv 1241 . . . . . . . . . . . 12
2118, 20cop 3370 . . . . . . . . . . 11  <. ,  >.
228, 21wceq 1242 . . . . . . . . . 10  <. ,  >.
2316, 22wa 97 . . . . . . . . 9  <. ,  >.  <. ,  >.
24 cpp 6277 . . . . . . . . . . 11  +P.
2512, 20, 24co 5455 . . . . . . . . . 10 
+P.
2614, 18, 24co 5455 . . . . . . . . . 10 
+P.
2725, 26wceq 1242 . . . . . . . . 9  +P.  +P.
2823, 27wa 97 . . . . . . . 8  <. ,  >.  <. ,  >. 
+P.  +P.
2928, 19wex 1378 . . . . . . 7  <. ,  >.  <. ,  >. 
+P.  +P.
3029, 17wex 1378 . . . . . 6  <. ,  >.  <. ,  >.  +P.  +P.
3130, 13wex 1378 . . . . 5  <. ,  >.  <. ,  >. 
+P.  +P.
3231, 11wex 1378 . . . 4 
<. ,  >.  <. ,  >.  +P.  +P.
3310, 32wa 97 . . 3  P.  X.  P.  P.  X.  P.  <. ,  >.  <. ,  >. 
+P.  +P.
3433, 2, 7copab 3808 . 2  { <. ,  >.  |  P.  X.  P.  P.  X.  P.  <. ,  >.  <. ,  >. 
+P.  +P.  }
351, 34wceq 1242 1  ~R  { <. , 
>.  |  P.  X.  P.  P.  X.  P. 
<. ,  >.  <. ,  >.  +P.  +P.  }
Colors of variables: wff set class
This definition is referenced by:  enrbreq  6662  enrer  6663  enrex  6665  prsrlem1  6670
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