Definition df-2nd 7169

Description: Define a function that extracts the second member, or ordinate, of an ordered pair. Theorem op2nd 7177 proves that it does this. For example, ( 2nd ` <. 3 , 4 >. ) = 4. Equivalent to Definition 5.13 (ii) of [Monk1] p. 52 (compare op2nda 5620 and op2ndb 5619). The notation is the same as Monk's. (Contributed by NM, 9-Oct-2004.)

Assertion

Ref	Expression
df-2nd	|- 2nd = ( x e. _V |-> U. ran { x } )

Detailed syntax breakdown of Definition df-2nd

Step	Hyp	Ref	Expression
1		c2nd 7167	. 2 class 2nd
2		vx	. . 3 setvar x
3		cvv 3200	. . 3 class _V
4	2	cv 1482	. . . . . 6 class x
5	4	csn 4177	. . . . 5 class { x }
6	5	crn 5115	. . . 4 class ran { x }
7	6	cuni 4436	. . 3 class U. ran { x }
8	2, 3, 7	cmpt 4729	. 2 class ( x e. _V |-> U. ran { x } )
9	1, 8	wceq 1483	1 wff 2nd = ( x e. _V |-> U. ran { x } )

This definition is referenced by:  2ndval  7171  fo2nd  7189  f2ndres  7191  hashf1rn  13142  hashf1rnOLD  13143