Theorem opeq1i

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

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

Proof

Step	Hyp	Ref	Expression
1		opeq1i.1	$$⊢A=B$$
2		opeq1	$$⊢A=B\to ⟨A,C⟩=⟨B,C⟩$$
3	1 2	ax-mp	$$⊢⟨A,C⟩=⟨B,C⟩$$