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Definition df-mp 8853
 Description: Define multiplication on positive reals. This is a "temporary" set used in the construction of complex numbers df-c 8988, and is intended to be used only by the construction. From Proposition 9-3.7 of [Gleason] p. 124. (Contributed by NM, 18-Nov-1995.) (New usage is discouraged.)
Assertion
Ref Expression
df-mp
Distinct variable group:   ,,,,

Detailed syntax breakdown of Definition df-mp
StepHypRef Expression
1 cmp 8729 . 2
2 vx . . 3
3 vy . . 3
4 cnp 8726 . . 3
5 vw . . . . . . . 8
65cv 1651 . . . . . . 7
7 vv . . . . . . . . 9
87cv 1651 . . . . . . . 8
9 vu . . . . . . . . 9
109cv 1651 . . . . . . . 8
11 cmq 8723 . . . . . . . 8
128, 10, 11co 6073 . . . . . . 7
136, 12wceq 1652 . . . . . 6
143cv 1651 . . . . . 6
1513, 9, 14wrex 2698 . . . . 5
162cv 1651 . . . . 5
1715, 7, 16wrex 2698 . . . 4
1817, 5cab 2421 . . 3
192, 3, 4, 4, 18cmpt2 6075 . 2
201, 19wceq 1652 1
 Colors of variables: wff set class This definition is referenced by:  mpv  8880  dmmp  8882  mulclprlem  8888  mulclpr  8889  mulasspr  8893  distrlem1pr  8894  distrlem4pr  8895  distrlem5pr  8896  1idpr  8898  reclem3pr  8918  reclem4pr  8919
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