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Definition df-2nd 5970
Description: Define a function that extracts the second member, or ordinate, of an ordered pair. Theorem op2nd 5976 proves that it does this. For example, (2nd ‘⟨ 3 , 4 ) = 4 . Equivalent to Definition 5.13 (ii) of [Monk1] p. 52 (compare op2nda 4959 and op2ndb 4958). 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 5968 . 2 class 2nd
2 vx . . 3 setvar 𝑥
3 cvv 2641 . . 3 class V
42cv 1298 . . . . . 6 class 𝑥
54csn 3474 . . . . 5 class {𝑥}
65crn 4478 . . . 4 class ran {𝑥}
76cuni 3683 . . 3 class ran {𝑥}
82, 3, 7cmpt 3929 . 2 class (𝑥 ∈ V ↦ ran {𝑥})
91, 8wceq 1299 1 wff 2nd = (𝑥 ∈ V ↦ ran {𝑥})
Colors of variables: wff set class
This definition is referenced by:  2ndvalg  5972  fo2nd  5987  f2ndres  5989  fihashf1rn  10376
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