Theorem oteq1

Description: Equality theorem for ordered triples. (Contributed by NM, 3-Apr-2015)

	Ref	Expression
Assertion	oteq1	$$⊢A=B\to ⟨A,C,D⟩=⟨B,C,D⟩$$

Proof

Step	Hyp	Ref	Expression
1		opeq1	$$⊢A=B\to ⟨A,C⟩=⟨B,C⟩$$
2	1	opeq1d	$$⊢A=B\to ⟨⟨A,C⟩,D⟩=⟨⟨B,C⟩,D⟩$$
3		df-ot	$$⊢⟨A,C,D⟩=⟨⟨A,C⟩,D⟩$$
4		df-ot	$$⊢⟨B,C,D⟩=⟨⟨B,C⟩,D⟩$$
5	2 3 4	3eqtr4g	$$⊢A=B\to ⟨A,C,D⟩=⟨B,C,D⟩$$