Theorem opeq1d

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

	Ref	Expression
Hypothesis	opeq1d.1	$$⊢\phi \to A=B$$
Assertion	opeq1d	$$⊢\phi \to ⟨A,C⟩=⟨B,C⟩$$

Proof

Step	Hyp	Ref	Expression
1		opeq1d.1	$$⊢\phi \to A=B$$
2		opeq1	$$⊢A=B\to ⟨A,C⟩=⟨B,C⟩$$
3	1 2	syl	$$⊢\phi \to ⟨A,C⟩=⟨B,C⟩$$