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Definition df-vtx 39253
Description: Define the function mapping a graph to the set of its vertices. This definition is very general: It defines the set of vertices for any ordered pair as its first component, and for any other class as its "base set". It is meaningful, however, only if the ordered pair represents a graph resp. the class is an extensible structure representing a graph. (Contributed by AV, 9-Jan-2020.) (Revised by AV, 20-Sep-2020.)
Assertion
Ref Expression
df-vtx  |- Vtx  =  ( g  e.  _V  |->  if ( g  e.  ( _V  X.  _V ) ,  ( 1st `  g
) ,  ( Base `  g ) ) )

Detailed syntax breakdown of Definition df-vtx
StepHypRef Expression
1 cvtx 39251 . 2  class Vtx
2 vg . . 3  setvar  g
3 cvv 3031 . . 3  class  _V
42cv 1451 . . . . 5  class  g
53, 3cxp 4837 . . . . 5  class  ( _V 
X.  _V )
64, 5wcel 1904 . . . 4  wff  g  e.  ( _V  X.  _V )
7 c1st 6810 . . . . 5  class  1st
84, 7cfv 5589 . . . 4  class  ( 1st `  g )
9 cbs 15199 . . . . 5  class  Base
104, 9cfv 5589 . . . 4  class  ( Base `  g )
116, 8, 10cif 3872 . . 3  class  if ( g  e.  ( _V 
X.  _V ) ,  ( 1st `  g ) ,  ( Base `  g
) )
122, 3, 11cmpt 4454 . 2  class  ( g  e.  _V  |->  if ( g  e.  ( _V 
X.  _V ) ,  ( 1st `  g ) ,  ( Base `  g
) ) )
131, 12wceq 1452 1  wff Vtx  =  ( g  e.  _V  |->  if ( g  e.  ( _V  X.  _V ) ,  ( 1st `  g
) ,  ( Base `  g ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  vtxval  39255
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