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Definition df-disj 3996
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  e.  A B  <->  A. y E* x  e.  A
y  e.  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  set  x
2 cA . . 3  class  A
3 cB . . 3  class  B
41, 2, 3wdisj 3995 . 2  wff Disj  x  e.  A B
5 vy . . . . . 6  set  y
65cv 1623 . . . . 5  class  y
76, 3wcel 1685 . . . 4  wff  y  e.  B
87, 1, 2wrmo 2548 . . 3  wff  E* x  e.  A y  e.  B
98, 5wal 1528 . 2  wff  A. y E* x  e.  A
y  e.  B
104, 9wb 178 1  wff  (Disj  x  e.  A B  <->  A. y E* x  e.  A
y  e.  B )
Colors of variables: wff set class
This definition is referenced by:  dfdisj2  3997  disjss2  3998  cbvdisj  4005  nfdisj  4007  nfdisj1  4008  disjor  4009  invdisj  4014  disjiun  4015
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