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, (2^nd ‘⟨ 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

Step	Hyp	Ref	Expression
1		c2nd 5708	. 2 class 2nd
2		vx	. . 3 setvar x
3		cvv 2551	. . 3 class V
4	2	cv 1241	. . . . . 6 class x
5	4	csn 3367	. . . . 5 class {x}
6	5	crn 4289	. . . 4 class ran {x}
7	6	cuni 3571	. . 3 class ∪ ran {x}
8	2, 3, 7	cmpt 3809	. 2 class (x ∈ V ↦ ∪ ran {x})
9	1, 8	wceq 1242	1 wff 2nd = (x ∈ V ↦ ∪ ran {x})

This definition is referenced by:  2ndvalg  5712  fo2nd  5727  f2ndres  5729