Theorem opeq12i

Description: Equality inference for ordered pairs. (Contributed by NM, 16-Dec-2006) (Proof shortened by Eric Schmidt, 4-Apr-2007)

	Ref	Expression
Hypotheses	opeq1i.1	$$⊢A=B$$
	opeq12i.2	$$⊢C=D$$
Assertion	opeq12i	$$⊢⟨A,C⟩=⟨B,D⟩$$

Proof

Step	Hyp	Ref	Expression
1		opeq1i.1	$$⊢A=B$$
2		opeq12i.2	$$⊢C=D$$
3		opeq12	$$⊢\left(A=B\wedge C=D\right)\to ⟨A,C⟩=⟨B,D⟩$$
4	1 2 3	mp2an	$$⊢⟨A,C⟩=⟨B,D⟩$$