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Definition df-2nd 7211
Description: Define a function that extracts the second member, or ordinate, of an ordered pair. Theorem op2nd 7219 proves that it does this. For example, (2nd ‘⟨3, 4⟩) = 4. Equivalent to Definition 5.13 (ii) of [Monk1] p. 52 (compare op2nda 5658 and op2ndb 5657). 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 7209 . 2 class 2nd
2 vx . . 3 setvar 𝑥
3 cvv 3231 . . 3 class V
42cv 1522 . . . . . 6 class 𝑥
54csn 4210 . . . . 5 class {𝑥}
65crn 5144 . . . 4 class ran {𝑥}
76cuni 4468 . . 3 class ran {𝑥}
82, 3, 7cmpt 4762 . 2 class (𝑥 ∈ V ↦ ran {𝑥})
91, 8wceq 1523 1 wff 2nd = (𝑥 ∈ V ↦ ran {𝑥})
Colors of variables: wff setvar class
This definition is referenced by:  2ndval  7213  fo2nd  7231  f2ndres  7235  hashf1rn  13181
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