I believe the following nice statement is true, but I cannot find a reference or proof it myself.
In a 2-category(i.e., bicategory), the composition of composable 2-cells is unambiguously defined.
Where 2-cells are 2-commutative triangles (other shape will not give more information), "composable" is not easy to say in simple words but it is easy to imagine.
Special cases of this statement include vertical composition of 2-morphisms are associative and the exchange law of vertical composition and horizontal composition.
Any comments or references would be appreciated. Thank you guys!