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Definition df-2nd 6336
Description: Define a function that extracts the second member, or ordinate, of an ordered pair. Theorem op2nd 6342 proves that it does this. For example,  ( 2nd ` 
<. 3 ,  4
>. )  =  4. Equivalent to Definition 5.13 (ii) of [Monk1] p. 52 (compare op2nda 5340 and op2ndb 5339). 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
StepHypRef Expression
1 c2nd 6334 . 2  class  2nd
2 vx . . 3  set  x
3 cvv 2943 . . 3  class  _V
42cv 1651 . . . . . 6  class  x
54csn 3801 . . . . 5  class  { x }
65crn 4865 . . . 4  class  ran  {
x }
76cuni 4002 . . 3  class  U. ran  { x }
82, 3, 7cmpt 4253 . 2  class  ( x  e.  _V  |->  U. ran  { x } )
91, 8wceq 1652 1  wff  2nd  =  ( x  e.  _V  |->  U.
ran  { x } )
Colors of variables: wff set class
This definition is referenced by:  2ndval  6338  fo2nd  6353  f2ndres  6355  hashf1rn  11619
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