Theorem oteq1d

Description: Equality deduction for ordered triples. (Contributed by Mario Carneiro, 11-Jan-2017)

	Ref	Expression
Hypothesis	oteq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	oteq1d	⊢ ( 𝜑 → ⟨ 𝐴 , 𝐶 , 𝐷 ⟩ = ⟨ 𝐵 , 𝐶 , 𝐷 ⟩ )

Proof

Step	Hyp	Ref	Expression
1		oteq1d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		oteq1	⊢ ( 𝐴 = 𝐵 → ⟨ 𝐴 , 𝐶 , 𝐷 ⟩ = ⟨ 𝐵 , 𝐶 , 𝐷 ⟩ )
3	1 2	syl	⊢ ( 𝜑 → ⟨ 𝐴 , 𝐶 , 𝐷 ⟩ = ⟨ 𝐵 , 𝐶 , 𝐷 ⟩ )