Definition df-2nd 3088

Description: Define a function that extracts the second member of an ordered pair. Equivalent to Definition 5.13 (ii) of [Monk1] p. 52 (compare op2ndb 2638 and op2nda 2639).

Assertion

Ref	Expression
df-2nd	⊢ 2nd = {⟨x, y⟩∣y = ∪ran {x}}

Distinct variable group(s):   x,y

Detailed syntax breakdown of Definition df-2nd

Step	Hyp	Ref	Expression
1		c2nd 3086	. 2 class 2nd
2		vy	. . . . 5 set y
3	2	cv 1089	. . . 4 class y
4		vx	. . . . . . . 8 set x
5	4	cv 1089	. . . . . . 7 class x
6	5	csn 1808	. . . . . 6 class {x}
7	6	crn 2411	. . . . 5 class ran {x}
8	7	cuni 1919	. . . 4 class ∪ran {x}
9	3, 8	wceq 1091	. . 3 wff y = ∪ran {x}
10	9, 4, 2	copab 2055	. 2 class {⟨x, y⟩∣y = ∪ran {x}}
11	1, 10	wceq 1091	1 wff 2nd = {⟨x, y⟩∣y = ∪ran {x}}

This definition is referenced by:  2ndval 3090  fo2nd 3095

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