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Definition df-2nd 5710
Description: Define a function that extracts the second member, or ordinate, of an ordered pair. Theorem op2nd 5716 proves that it does this. For example, (2nd ‘⟨ 3 , 4 ) = 4 . Equivalent to Definition 5.13 (ii) of [Monk1] p. 52 (compare op2nda 4748 and op2ndb 4747). The notation is the same as Monk's. (Contributed by NM, 9-Oct-2004.)
Assertion
Ref Expression
df-2nd 2nd = (x V ↦ ran {x})

Detailed syntax breakdown of Definition df-2nd
StepHypRef Expression
1 c2nd 5708 . 2 class 2nd
2 vx . . 3 setvar x
3 cvv 2551 . . 3 class V
42cv 1241 . . . . . 6 class x
54csn 3367 . . . . 5 class {x}
65crn 4289 . . . 4 class ran {x}
76cuni 3571 . . 3 class ran {x}
82, 3, 7cmpt 3809 . 2 class (x V ↦ ran {x})
91, 8wceq 1242 1 wff 2nd = (x V ↦ ran {x})
Colors of variables: wff set class
This definition is referenced by:  2ndvalg  5712  fo2nd  5727  f2ndres  5729
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