Theorem op2nd

Description: Extract the second member of an ordered pair. (Contributed by NM, 5-Oct-2004)

	Ref	Expression
Hypotheses	op1st.1	$$⊢A\in \mathrm{V}$$
	op1st.2	$$⊢B\in \mathrm{V}$$
Assertion	op2nd	$$⊢2^{nd}\left(⟨A,B⟩\right)=B$$

Proof

Step	Hyp	Ref	Expression
1		op1st.1	$$⊢A\in \mathrm{V}$$
2		op1st.2	$$⊢B\in \mathrm{V}$$
3		2ndval	$$⊢2^{nd}\left(⟨A,B⟩\right)=\bigcup \mathrm{ran}\left\{⟨A,B⟩\right\}$$
4	1 2	op2nda	$$⊢\bigcup \mathrm{ran}\left\{⟨A,B⟩\right\}=B$$
5	3 4	eqtri	$$⊢2^{nd}\left(⟨A,B⟩\right)=B$$