let n, m be Nat; for D being non empty set
for M1, M2 being Matrix of n,m,D st ( for i, j being Nat st [i,j] in Indices M1 holds
M1 * (i,j) = M2 * (i,j) ) holds
M1 = M2
let D be non empty set ; for M1, M2 being Matrix of n,m,D st ( for i, j being Nat st [i,j] in Indices M1 holds
M1 * (i,j) = M2 * (i,j) ) holds
M1 = M2
let M1, M2 be Matrix of n,m,D; ( ( for i, j being Nat st [i,j] in Indices M1 holds
M1 * (i,j) = M2 * (i,j) ) implies M1 = M2 )
A1:
len M1 = n
by Th25;
A2:
len M2 = n
by Th25;
assume
for i, j being Nat st [i,j] in Indices M1 holds
M1 * (i,j) = M2 * (i,j)
; M1 = M2
hence
M1 = M2
by A1, A2, A3, Th21; verum