Theorem oteq3

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

	Ref	Expression
Assertion	oteq3	$$⊢A=B\to ⟨C,D,A⟩=⟨C,D,B⟩$$

Proof

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