Equality of Ordered Triples/Proof 1

Example of Equality of Ordered Tuples

Let:

$\tuple {a_1, a_2, a_3}$ and $\tuple {b_1, b_2, b_3}$

be ordered triples.

Then:

$\tuple {a_1, a_2, a_3} = \tuple {b_1, b_2, b_3}$

if and only if:

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

Proof

A special case of Equality of Ordered Tuples for $m = n = 3$.

$\blacksquare$