Definition df-vtx 16434

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 16432	. 2 class Vtx
2		vg	. . 3 setvar g
3		cvv 2821	. . 3 class _V
4	2	cv 1401	. . . . 5 class g
5	3, 3	cxp 4772	. . . . 5 class ( _V X. _V )
6	4, 5	wcel 2209	. . . 4 wff g e. ( _V X. _V )
7		c1st 6372	. . . . 5 class 1st
8	4, 7	cfv 5377	. . . 4 class ( 1st ` g )
9		cbs 13404	. . . . 5 class Base
10	4, 9	cfv 5377	. . . 4 class ( Base ` g )
11	6, 8, 10	cif 3638	. . 3 class if ( g e. ( _V X. _V ) , ( 1st ` g ) , ( Base ` g ) )
12	2, 3, 11	cmpt 4192	. 2 class ( g e. _V |-> if ( g e. ( _V X. _V ) , ( 1st ` g ) , ( Base ` g ) ) )
13	1, 12	wceq 1402	1 wff Vtx = ( g e. _V |-> if ( g e. ( _V X. _V ) , ( 1st ` g ) , ( Base ` g ) ) )

This definition is used by:  vtxvalg  16436  1vgrex  16440  wlkreslem  16798  clwwlknonmpo  16848  trlsegvdegfi  16887  eupth2lem3lem1fi  16888  eupth2lem3lem2fi  16889  eupth2lem3lem6fi  16891  eupth2lem3lem4fi  16893