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Definition df-2nd 5796
Description: Define a function that extracts the second member, or ordinate, of an ordered pair. Theorem op2nd 5802 proves that it does this. For example, (2nd ‘⟨ 3 , 4 ) = 4 . Equivalent to Definition 5.13 (ii) of [Monk1] p. 52 (compare op2nda 4833 and op2ndb 4832). 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 5794 . 2 class 2nd
2 vx . . 3 setvar 𝑥
3 cvv 2574 . . 3 class V
42cv 1258 . . . . . 6 class 𝑥
54csn 3403 . . . . 5 class {𝑥}
65crn 4374 . . . 4 class ran {𝑥}
76cuni 3608 . . 3 class ran {𝑥}
82, 3, 7cmpt 3846 . 2 class (𝑥 ∈ V ↦ ran {𝑥})
91, 8wceq 1259 1 wff 2nd = (𝑥 ∈ V ↦ ran {𝑥})
Colors of variables: wff set class
This definition is referenced by:  2ndvalg  5798  fo2nd  5813  f2ndres  5815
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