Definition df-vtx 15852

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 15850	. 2 class Vtx
2		vg	. . 3 setvar g
3		cvv 2800	. . 3 class _V
4	2	cv 1394	. . . . 5 class g
5	3, 3	cxp 4719	. . . . 5 class ( _V X. _V )
6	4, 5	wcel 2200	. . . 4 wff g e. ( _V X. _V )
7		c1st 6294	. . . . 5 class 1st
8	4, 7	cfv 5322	. . . 4 class ( 1st ` g )
9		cbs 13069	. . . . 5 class Base
10	4, 9	cfv 5322	. . . 4 class ( Base ` g )
11	6, 8, 10	cif 3603	. . 3 class if ( g e. ( _V X. _V ) , ( 1st ` g ) , ( Base ` g ) )
12	2, 3, 11	cmpt 4146	. 2 class ( g e. _V |-> if ( g e. ( _V X. _V ) , ( 1st ` g ) , ( Base ` g ) ) )
13	1, 12	wceq 1395	1 wff Vtx = ( g e. _V |-> if ( g e. ( _V X. _V ) , ( 1st ` g ) , ( Base ` g ) ) )

This definition is referenced by:  vtxvalg  15854  1vgrex  15858  wlkreslem  16164  clwwlknonmpo  16213