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Definition df-xdiv 28957
 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 28956 . 2 class /𝑒
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cxr 9952 . . 3 class *
5 cr 9814 . . . 4 class
6 cc0 9815 . . . . 5 class 0
76csn 4125 . . . 4 class {0}
85, 7cdif 3537 . . 3 class (ℝ ∖ {0})
93cv 1474 . . . . . 6 class 𝑦
10 vz . . . . . . 7 setvar 𝑧
1110cv 1474 . . . . . 6 class 𝑧
12 cxmu 11821 . . . . . 6 class ·e
139, 11, 12co 6549 . . . . 5 class (𝑦 ·e 𝑧)
142cv 1474 . . . . 5 class 𝑥
1513, 14wceq 1475 . . . 4 wff (𝑦 ·e 𝑧) = 𝑥
1615, 10, 4crio 6510 . . 3 class (𝑧 ∈ ℝ* (𝑦 ·e 𝑧) = 𝑥)
172, 3, 4, 8, 16cmpt2 6551 . 2 class (𝑥 ∈ ℝ*, 𝑦 ∈ (ℝ ∖ {0}) ↦ (𝑧 ∈ ℝ* (𝑦 ·e 𝑧) = 𝑥))
181, 17wceq 1475 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  28958
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