Theorem opeq2d

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

	Ref	Expression
Hypothesis	opeq1d.1	$$⊢\phi \to A=B$$
Assertion	opeq2d	$$⊢\phi \to ⟨C,A⟩=⟨C,B⟩$$

Proof

Step	Hyp	Ref	Expression
1		opeq1d.1	$$⊢\phi \to A=B$$
2		opeq2	$$⊢A=B\to ⟨C,A⟩=⟨C,B⟩$$
3	1 2	syl	$$⊢\phi \to ⟨C,A⟩=⟨C,B⟩$$