Theorem opeq2i

Description: Equality inference for ordered pairs. (Contributed by NM, 16-Dec-2006)

	Ref	Expression
Hypothesis	opeq1i.1	$$⊢A=B$$
Assertion	opeq2i	$$⊢⟨C,A⟩=⟨C,B⟩$$

Proof

Step	Hyp	Ref	Expression
1		opeq1i.1	$$⊢A=B$$
2		opeq2	$$⊢A=B\to ⟨C,A⟩=⟨C,B⟩$$
3	1 2	ax-mp	$$⊢⟨C,A⟩=⟨C,B⟩$$