Note (we should) that here the objective is to recalculate an equation
for s2 under the symmetrized conditions.
   And this means that d1fr1=x7, or d2fr2=x8, or d3fr3=x9 can be taken 
to be the variable "at issue". So let's choose x9 ( -> y9 ) as the variable
in question (as a variance on previous use of x7 (or d1fr1)).

vvtoss = {d1f2 -> s1, d1f3 -> s1, d2f1 -> s1, d2f3 -> s1, d3f1 -> s1, 
     d3f2 -> s1, d1fr1 -> s2, d2fr2 -> s2, d3fr3 -> s2, dr1v2 -> s3, 
     dr1v3 -> s3, dr2v1 -> s3, dr2v3 -> s3, dr3v1 -> s3, dr3v2 -> s3}

vvtoxx = {d1f2 -> x1, d1f3 -> x2, d2f1 -> x3, d2f3 -> x4, d3f1 -> x5, 
     d3f2 -> x6, d1fr1 -> x7, d2fr2 -> x8, d3fr3 -> x9, dr1v2 -> x10, 
     dr1v3 -> x11, dr2v1 -> x12, dr2v3 -> x13, dr3v1 -> x14, dr3v2 -> x15}
 
xxtovv = {x1 -> d1f2, x2 -> d1f3, x3 -> d2f1, x4 -> d2f3, x5 -> d3f1, 
     x6 -> d3f2, x7 -> d1fr1, x8 -> d2fr2, x9 -> d3fr3, x10 -> dr1v2, 
     x11 -> dr1v3, x12 -> dr2v1, x13 -> dr2v3, x14 -> dr3v1, x15 -> dr3v2}
 
xxtoss = {x1 -> s1, x2 -> s1, x3 -> s1, x4 -> s1, x5 -> s1, x6 -> s1, 
     x7 -> s2, x8 -> s2, x9 -> s2, x10 -> s3, x11 -> s3, x12 -> s3, 
     x13 -> s3, x14 -> s3, x15 -> s3}