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Definition df-mgra 25812
Description: Definition of a directed multi graph. Loops are allowed and there may be more than one edge between the same pair of vertices. Isolated points are allowed. (Contributed by FL, 10-Jan-2008.)
Assertion
Ref Expression
df-mgra  |-  Dgra  =  { <. <. d ,  c
>. ,  u >.  |  ( d : dom  d
--> u  /\  c : dom  d --> u ) }
Distinct variable group:    c, d, u

Detailed syntax breakdown of Definition df-mgra
StepHypRef Expression
1 cmgra 25811 . 2  class  Dgra
2 vd . . . . . . 7  set  d
32cv 1631 . . . . . 6  class  d
43cdm 4705 . . . . 5  class  dom  d
5 vu . . . . . 6  set  u
65cv 1631 . . . . 5  class  u
74, 6, 3wf 5267 . . . 4  wff  d : dom  d --> u
8 vc . . . . . 6  set  c
98cv 1631 . . . . 5  class  c
104, 6, 9wf 5267 . . . 4  wff  c : dom  d --> u
117, 10wa 358 . . 3  wff  ( d : dom  d --> u  /\  c : dom  d
--> u )
1211, 2, 8, 5coprab 5875 . 2  class  { <. <.
d ,  c >. ,  u >.  |  (
d : dom  d --> u  /\  c : dom  d
--> u ) }
131, 12wceq 1632 1  wff  Dgra  =  { <. <. d ,  c
>. ,  u >.  |  ( d : dom  d
--> u  /\  c : dom  d --> u ) }
Colors of variables: wff set class
This definition is referenced by:  ismgra  25813
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