Definition df-2nd 4080

Description: Define a function that extracts the second member of an ordered pair. Theorem op2nd 4086 proves that it does this. Equivalent to Definition 5.13 (ii) of [Monk1] p. 52 (compare op2nda 3452 and op2ndb 3451). The notation is the same as Monk's.

Assertion

Ref	Expression
df-2nd	|- 2nd = {<.x, y>. | y = U.ran { x}}

Distinct variable group:   x,y

Detailed syntax breakdown of Definition df-2nd

Step	Hyp	Ref	Expression
1		c2nd 4078	. 2 class 2nd
2		vy	. . . . 5 set y
3	2	cv 955	. . . 4 class y
4		vx	. . . . . . . 8 set x
5	4	cv 955	. . . . . . 7 class x
6	5	csn 2409	. . . . . 6 class {x}
7	6	crn 3171	. . . . 5 class ran { x}
8	7	cuni 2503	. . . 4 class U.ran { x}
9	3, 8	wceq 956	. . 3 wff y = U.ran { x}
10	9, 4, 2	copab 2666	. 2 class {<.x, y>. | y = U.ran { x}}
11	1, 10	wceq 956	1 wff 2nd = {<.x, y>. | y = U.ran { x}}

This definition is referenced by:  2ndval 4082  fo2nd 4092  f2ndres 4094

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