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Definition df-dcin 11051
Description: Define decidability of a class in another. (Contributed by BJ, 19-Feb-2022.)
Assertion
Ref Expression
df-dcin (𝐴 DECIDin 𝐵 ↔ ∀𝑥𝐵 DECID 𝑥𝐴)
Distinct variable groups:   𝑥,𝐴   𝑥,𝐵

Detailed syntax breakdown of Definition df-dcin
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cB . . 3 class 𝐵
31, 2wdcin 11050 . 2 wff 𝐴 DECIDin 𝐵
4 vx . . . . . 6 setvar 𝑥
54cv 1286 . . . . 5 class 𝑥
65, 1wcel 1436 . . . 4 wff 𝑥𝐴
76wdc 778 . . 3 wff DECID 𝑥𝐴
87, 4, 2wral 2355 . 2 wff 𝑥𝐵 DECID 𝑥𝐴
93, 8wb 103 1 wff (𝐴 DECIDin 𝐵 ↔ ∀𝑥𝐵 DECID 𝑥𝐴)
Colors of variables: wff set class
This definition is referenced by:  decidi  11052  decidr  11053  sumdc2  11056
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