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Definition df-enq 6445
 Description: Define equivalence relation for positive fractions. This is a "temporary" set used in the construction of complex numbers, and is intended to be used only by the construction. From Proposition 9-2.1 of [Gleason] p. 117. (Contributed by NM, 27-Aug-1995.)
Assertion
Ref Expression
df-enq
Distinct variable group:   ,,,,,

Detailed syntax breakdown of Definition df-enq
StepHypRef Expression
1 ceq 6377 . 2
2 vx . . . . . . 7
32cv 1242 . . . . . 6
4 cnpi 6370 . . . . . . 7
54, 4cxp 4343 . . . . . 6
63, 5wcel 1393 . . . . 5
7 vy . . . . . . 7
87cv 1242 . . . . . 6
98, 5wcel 1393 . . . . 5
106, 9wa 97 . . . 4
11 vz . . . . . . . . . . . . 13
1211cv 1242 . . . . . . . . . . . 12
13 vw . . . . . . . . . . . . 13
1413cv 1242 . . . . . . . . . . . 12
1512, 14cop 3378 . . . . . . . . . . 11
163, 15wceq 1243 . . . . . . . . . 10
17 vv . . . . . . . . . . . . 13
1817cv 1242 . . . . . . . . . . . 12
19 vu . . . . . . . . . . . . 13
2019cv 1242 . . . . . . . . . . . 12
2118, 20cop 3378 . . . . . . . . . . 11
228, 21wceq 1243 . . . . . . . . . 10
2316, 22wa 97 . . . . . . . . 9
24 cmi 6372 . . . . . . . . . . 11
2512, 20, 24co 5512 . . . . . . . . . 10
2614, 18, 24co 5512 . . . . . . . . . 10
2725, 26wceq 1243 . . . . . . . . 9
2823, 27wa 97 . . . . . . . 8
2928, 19wex 1381 . . . . . . 7
3029, 17wex 1381 . . . . . 6
3130, 13wex 1381 . . . . 5
3231, 11wex 1381 . . . 4
3310, 32wa 97 . . 3
3433, 2, 7copab 3817 . 2
351, 34wceq 1243 1
 Colors of variables: wff set class This definition is referenced by:  enqbreq  6454  enqer  6456  enqex  6458  addpipqqs  6468  mulpipqqs  6471  enq0enq  6529
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