Theorem opeq1d

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

	Ref	Expression
Hypothesis	opeq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	opeq1d	⊢ ( 𝜑 → ⟨ 𝐴 , 𝐶 ⟩ = ⟨ 𝐵 , 𝐶 ⟩ )

Proof

Step	Hyp	Ref	Expression
1		opeq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		opeq1	⊢ ( 𝐴 = 𝐵 → ⟨ 𝐴 , 𝐶 ⟩ = ⟨ 𝐵 , 𝐶 ⟩ )
3	1 2	syl	⊢ ( 𝜑 → ⟨ 𝐴 , 𝐶 ⟩ = ⟨ 𝐵 , 𝐶 ⟩ )