Quick question about simplifying a circuit

[STEMucator]

Homework Statement

I want to see if I'm reducing the following circuit correctly.

Homework Equations

The Attempt at a Solution

The two outer resistors are in series:

$R_{56} = R_5 + R_6$

Now the outer resistors would be directly wired on each end after simplifying. Hence:

$R_{456} = (\frac{1}{R_4} + \frac{1}{R_{56}})^{-1}$

Series again:

$R_{2456} = R_2 + R_{456}$

Parallel:

$R_{32456} = (\frac{1}{R_3} + \frac{1}{R_{2456}})^{-1}$

Series:

$R_{132456} = R_1 + R_{32456}$

Now if we had the emf we could find the current and work backwards if needed.

 

[Orodruin]

Looks reasonable. Looking for the current i6 there may be easier ways though. They should all amount to the same in the end.