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

Step	Hyp	Ref	Expression
1		cvtx 39251	. 2 class Vtx
2		vg	. . 3 setvar g
3		cvv 3031	. . 3 class _V
4	2	cv 1451	. . . . 5 class g
5	3, 3	cxp 4837	. . . . 5 class ( _V X. _V )
6	4, 5	wcel 1904	. . . 4 wff g e. ( _V X. _V )
7		c1st 6810	. . . . 5 class 1st
8	4, 7	cfv 5589	. . . 4 class ( 1st ` g )
9		cbs 15199	. . . . 5 class Base
10	4, 9	cfv 5589	. . . 4 class ( Base ` g )
11	6, 8, 10	cif 3872	. . 3 class if ( g e. ( _V X. _V ) , ( 1st ` g ) , ( Base ` g ) )
12	2, 3, 11	cmpt 4454	. 2 class ( g e. _V |-> if ( g e. ( _V X. _V ) , ( 1st ` g ) , ( Base ` g ) ) )
13	1, 12	wceq 1452	1 wff Vtx = ( g e. _V |-> if ( g e. ( _V X. _V ) , ( 1st ` g ) , ( Base ` g ) ) )

This definition is referenced by:  vtxval  39255