Equality of Ordered Triples

Theorem
Let $A = \tuple {a_1, a_2, a_3}$ and $B = \tuple {b_1, b_2, b_3}$ be ordered triples.

Then:
 * $A = B$


 * $\forall i \in \set {1, 2, 3}: a_i = b_i$
 * $\forall i \in \set {1, 2, 3}: a_i = b_i$

Proof
From Equality of Ordered Pairs: