1 can be Expressed as Sum of 4 Distinct Unit Fractions in 6 Ways/Proof 2

Proof
From Sum of 4 Unit Fractions that equals 1:

This includes repeated unit fractions.

The full list is:

The result follows from inspection: solutions $(1)$, $(2)$, $(3)$, $(4)$, $(6)$ and $(7)$ are the only solutions of the above such that the denominators of the summands are distinct.