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	$$⊢2^{nd}=\left(x\in \mathrm{V}⟼\bigcup \mathrm{ran}\left\{x\right\}\right)$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		c2nd	$$class{2}^{nd}$$
1		vx	$$setvarx$$
2		cvv	$$class\mathrm{V}$$
3	1	cv	$$setvarx$$
4	3	csn	$$class\left\{x\right\}$$
5	4	crn	$$class\mathrm{ran}\left\{x\right\}$$
6	5	cuni	$$class\bigcup \mathrm{ran}\left\{x\right\}$$
7	1 2 6	cmpt	$$class\left(x\in \mathrm{V}⟼\bigcup \mathrm{ran}\left\{x\right\}\right)$$
8	0 7	wceq	$$wff{2}^{nd}=\left(x\in \mathrm{V}⟼\bigcup \mathrm{ran}\left\{x\right\}\right)$$