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Definition df-xdiv 30716
 Description: Define division over extended real numbers. (Contributed by Thierry Arnoux, 17-Dec-2016.)
Assertion
Ref Expression
df-xdiv /𝑒 = (𝑥 ∈ ℝ*, 𝑦 ∈ (ℝ ∖ {0}) ↦ (𝑧 ∈ ℝ* (𝑦 ·e 𝑧) = 𝑥))
Distinct variable group:   𝑥,𝑦,𝑧

Detailed syntax breakdown of Definition df-xdiv
StepHypRef Expression
1 cxdiv 30715 . 2 class /𝑒
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cxr 10712 . . 3 class *
5 cr 10574 . . . 4 class
6 cc0 10575 . . . . 5 class 0
76csn 4522 . . . 4 class {0}
85, 7cdif 3855 . . 3 class (ℝ ∖ {0})
93cv 1537 . . . . . 6 class 𝑦
10 vz . . . . . . 7 setvar 𝑧
1110cv 1537 . . . . . 6 class 𝑧
12 cxmu 12547 . . . . . 6 class ·e
139, 11, 12co 7150 . . . . 5 class (𝑦 ·e 𝑧)
142cv 1537 . . . . 5 class 𝑥
1513, 14wceq 1538 . . . 4 wff (𝑦 ·e 𝑧) = 𝑥
1615, 10, 4crio 7107 . . 3 class (𝑧 ∈ ℝ* (𝑦 ·e 𝑧) = 𝑥)
172, 3, 4, 8, 16cmpo 7152 . 2 class (𝑥 ∈ ℝ*, 𝑦 ∈ (ℝ ∖ {0}) ↦ (𝑧 ∈ ℝ* (𝑦 ·e 𝑧) = 𝑥))
181, 17wceq 1538 1 wff /𝑒 = (𝑥 ∈ ℝ*, 𝑦 ∈ (ℝ ∖ {0}) ↦ (𝑧 ∈ ℝ* (𝑦 ·e 𝑧) = 𝑥))
 Colors of variables: wff setvar class This definition is referenced by:  xdivval  30717
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