theorem Th39: :: MATRIX13:39

for D being non empty set
for i, j, m, n, m9, n9 being Nat
for A9 being Matrix of n9,m9,D
for nt being Element of n -tuples_on NAT
for mt being Element of m -tuples_on NAT st i in rng nt & [:(rng nt),(rng mt):] c= Indices A9 holds
ex nt1 being Element of n -tuples_on NAT st
( rng nt1 = ((rng nt) \ {i}) \/ {j} & Segm ((RLine (A9,i,(Line (A9,j)))),nt,mt) = Segm (A9,nt1,mt) )