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Definition df-imp 7277
 Description: Define multiplication on positive reals. Here we use a simple definition which is similar to df-iplp 7276 or the definition of multiplication on positive reals in Metamath Proof Explorer. This is as opposed to the more complicated definition of multiplication given in Section 11.2.1 of [HoTT], p. (varies), which appears to be motivated by handling negative numbers or handling modified Dedekind cuts in which locatedness is omitted. This is a "temporary" set used in the construction of complex numbers, and is intended to be used only by the construction. (Contributed by Jim Kingdon, 29-Sep-2019.)
Assertion
Ref Expression
df-imp
Distinct variable group:   ,,,,

Detailed syntax breakdown of Definition df-imp
StepHypRef Expression
1 cmp 7102 . 2
2 vx . . 3
3 vy . . 3
4 cnp 7099 . . 3
5 vr . . . . . . . . . 10
65cv 1330 . . . . . . . . 9
72cv 1330 . . . . . . . . . 10
8 c1st 6036 . . . . . . . . . 10
97, 8cfv 5123 . . . . . . . . 9
106, 9wcel 1480 . . . . . . . 8
11 vs . . . . . . . . . 10
1211cv 1330 . . . . . . . . 9
133cv 1330 . . . . . . . . . 10
1413, 8cfv 5123 . . . . . . . . 9
1512, 14wcel 1480 . . . . . . . 8
16 vq . . . . . . . . . 10
1716cv 1330 . . . . . . . . 9
18 cmq 7091 . . . . . . . . . 10
196, 12, 18co 5774 . . . . . . . . 9
2017, 19wceq 1331 . . . . . . . 8
2110, 15, 20w3a 962 . . . . . . 7
22 cnq 7088 . . . . . . 7
2321, 11, 22wrex 2417 . . . . . 6
2423, 5, 22wrex 2417 . . . . 5
2524, 16, 22crab 2420 . . . 4
26 c2nd 6037 . . . . . . . . . 10
277, 26cfv 5123 . . . . . . . . 9
286, 27wcel 1480 . . . . . . . 8
2913, 26cfv 5123 . . . . . . . . 9
3012, 29wcel 1480 . . . . . . . 8
3128, 30, 20w3a 962 . . . . . . 7
3231, 11, 22wrex 2417 . . . . . 6
3332, 5, 22wrex 2417 . . . . 5
3433, 16, 22crab 2420 . . . 4
3525, 34cop 3530 . . 3
362, 3, 4, 4, 35cmpo 5776 . 2
371, 36wceq 1331 1
 Colors of variables: wff set class This definition is referenced by:  mpvlu  7347  dmmp  7349  mulnqprl  7376  mulnqpru  7377  mulclpr  7380  mulnqprlemrl  7381  mulnqprlemru  7382  mulassprg  7389  distrlem1prl  7390  distrlem1pru  7391  distrlem4prl  7392  distrlem4pru  7393  distrlem5prl  7394  distrlem5pru  7395  1idprl  7398  1idpru  7399  recexprlem1ssl  7441  recexprlem1ssu  7442  recexprlemss1l  7443  recexprlemss1u  7444
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