Theorem oteq1d

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

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

Proof

Step	Hyp	Ref	Expression
1		oteq1d.1	$$⊢\phi \to A=B$$
2		oteq1	$$⊢A=B\to ⟨A,C,D⟩=⟨B,C,D⟩$$
3	1 2	syl	$$⊢\phi \to ⟨A,C,D⟩=⟨B,C,D⟩$$