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Definition df-disj 4398
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  setvar  x
2 cA . . 3  class  A
3 cB . . 3  class  B
41, 2, 3wdisj 4397 . 2  wff Disj  x  e.  A  B
5 vy . . . . . 6  setvar  y
65cv 1436 . . . . 5  class  y
76, 3wcel 1870 . . . 4  wff  y  e.  B
87, 1, 2wrmo 2785 . . 3  wff  E* x  e.  A  y  e.  B
98, 5wal 1435 . 2  wff  A. y E* x  e.  A  y  e.  B
104, 9wb 187 1  wff  (Disj  x  e.  A  B  <->  A. y E* x  e.  A  y  e.  B )
Colors of variables: wff setvar class
This definition is referenced by:  dfdisj2  4399  disjss2  4400  cbvdisj  4407  nfdisj1  4410  disjor  4411  disjiun  4417  cbvdisjf  28021  disjss1f  28022  disjorf  28028  disjin  28035  disjin2  28036  disjrdx  28040  ddemeas  28898  iccpartdisj  38150
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