Theorem oteq3d

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

	Ref	Expression
Hypothesis	oteq1d.1	$$⊢\phi \to A=B$$
Assertion	oteq3d	$$⊢\phi \to ⟨C,D,A⟩=⟨C,D,B⟩$$

Proof

Step	Hyp	Ref	Expression
1		oteq1d.1	$$⊢\phi \to A=B$$
2		oteq3	$$⊢A=B\to ⟨C,D,A⟩=⟨C,D,B⟩$$
3	1 2	syl	$$⊢\phi \to ⟨C,D,A⟩=⟨C,D,B⟩$$