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Definition df-cndprob 29821
 Description: Define the conditional probability. (Contributed by Thierry Arnoux, 14-Sep-2016.) (Revised by Thierry Arnoux, 21-Jan-2017.)
Assertion
Ref Expression
df-cndprob cprob = (𝑝 ∈ Prob ↦ (𝑎 ∈ dom 𝑝, 𝑏 ∈ dom 𝑝 ↦ ((𝑝‘(𝑎𝑏)) / (𝑝𝑏))))
Distinct variable group:   𝑎,𝑏,𝑝

Detailed syntax breakdown of Definition df-cndprob
StepHypRef Expression
1 ccprob 29820 . 2 class cprob
2 vp . . 3 setvar 𝑝
3 cprb 29796 . . 3 class Prob
4 va . . . 4 setvar 𝑎
5 vb . . . 4 setvar 𝑏
62cv 1474 . . . . 5 class 𝑝
76cdm 5038 . . . 4 class dom 𝑝
84cv 1474 . . . . . . 7 class 𝑎
95cv 1474 . . . . . . 7 class 𝑏
108, 9cin 3539 . . . . . 6 class (𝑎𝑏)
1110, 6cfv 5804 . . . . 5 class (𝑝‘(𝑎𝑏))
129, 6cfv 5804 . . . . 5 class (𝑝𝑏)
13 cdiv 10563 . . . . 5 class /
1411, 12, 13co 6549 . . . 4 class ((𝑝‘(𝑎𝑏)) / (𝑝𝑏))
154, 5, 7, 7, 14cmpt2 6551 . . 3 class (𝑎 ∈ dom 𝑝, 𝑏 ∈ dom 𝑝 ↦ ((𝑝‘(𝑎𝑏)) / (𝑝𝑏)))
162, 3, 15cmpt 4643 . 2 class (𝑝 ∈ Prob ↦ (𝑎 ∈ dom 𝑝, 𝑏 ∈ dom 𝑝 ↦ ((𝑝‘(𝑎𝑏)) / (𝑝𝑏))))
171, 16wceq 1475 1 wff cprob = (𝑝 ∈ Prob ↦ (𝑎 ∈ dom 𝑝, 𝑏 ∈ dom 𝑝 ↦ ((𝑝‘(𝑎𝑏)) / (𝑝𝑏))))
 Colors of variables: wff setvar class This definition is referenced by:  cndprobval  29822
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