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Metamath Proof Explorer

Definition df-2nd

Description: Define a function that extracts the second member, or ordinate, of an ordered pair. Theorem op2nd proves that it does this. For example, ( 2nd<. 3 , 4 >. ) = 4 . Equivalent to Definition 5.13 (ii) of Monk1 p. 52 (compare op2nda and op2ndb ). The notation is the same as Monk's. (Contributed by NM, 9-Oct-2004)

		Ref	Expression
	Assertion	df-2nd	\|- 2nd = ( x e. _V \|-> U. ran { x } )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		c2nd	\|- 2nd
1		vx	\|- x
2		cvv	\|- _V
3	1	cv	\|- x
4	3	csn	\|- { x }
5	4	crn	\|- ran { x }
6	5	cuni	\|- U. ran { x }
7	1 2 6	cmpt	\|- ( x e. _V \|-> U. ran { x } )
8	0 7	wceq	\|- 2nd = ( x e. _V \|-> U. ran { x } )