Theorem oteq2

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

	Ref	Expression
Assertion	oteq2	$$⊢A=B\to ⟨C,A,D⟩=⟨C,B,D⟩$$

Proof

Step	Hyp	Ref	Expression
1		opeq2	$$⊢A=B\to ⟨C,A⟩=⟨C,B⟩$$
2	1	opeq1d	$$⊢A=B\to ⟨⟨C,A⟩,D⟩=⟨⟨C,B⟩,D⟩$$
3		df-ot	$$⊢⟨C,A,D⟩=⟨⟨C,A⟩,D⟩$$
4		df-ot	$$⊢⟨C,B,D⟩=⟨⟨C,B⟩,D⟩$$
5	2 3 4	3eqtr4g	$$⊢A=B\to ⟨C,A,D⟩=⟨C,B,D⟩$$