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Definition df-disj 3737
Description: A collection of classes B(x) is disjoint when for each element y, it is in B(x) for at most one x. (Contributed by Mario Carneiro, 14-Nov-2016.) (Revised by NM, 16-Jun-2017.)
Assertion
Ref Expression
df-disj (Disj x A By∃*x A y B)
Distinct variable groups:   x,y   y,A   y,B
Allowed substitution hints:   A(x)   B(x)

Detailed syntax breakdown of Definition df-disj
StepHypRef Expression
1 vx . . 3 setvar x
2 cA . . 3 class A
3 cB . . 3 class B
41, 2, 3wdisj 3736 . 2 wff Disj x A B
5 vy . . . . . 6 setvar y
65cv 1241 . . . . 5 class y
76, 3wcel 1390 . . . 4 wff y B
87, 1, 2wrmo 2303 . . 3 wff ∃*x A y B
98, 5wal 1240 . 2 wff y∃*x A y B
104, 9wb 98 1 wff (Disj x A By∃*x A y B)
Colors of variables: wff set class
This definition is referenced by:  dfdisj2  3738  disjss2  3739  cbvdisj  3746  nfdisj1  3749
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