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 → ⟨ 𝐴 , 𝐶 ⟩ = ⟨ 𝐵 , 𝐶 ⟩ )
3	1 2	ax-mp	⊢ ⟨ 𝐴 , 𝐶 ⟩ = ⟨ 𝐵 , 𝐶 ⟩