let V be non empty set ; :: thesis: for m being Element of Maps V holds
( ( cod m <> {} or dom m = {} ) & m `2 is Function of (dom m),(cod m) )
let m be Element of Maps V; :: thesis: ( ( cod m <> {} or dom m = {} ) & m `2 is Function of (dom m),(cod m) )
consider f being Element of Funcs V, A, B being Element of V such that
A1: m = [[A,B],f] and
A2: ( ( B = {} implies A = {} ) & f is Function of A,B ) by Th4;
A3: m = [[(dom m),(cod m)],(m `2)] by Th8;
then ( f = m `2 & A = dom m ) by A1, Lm1, ZFMISC_1:33;
hence ( ( cod m <> {} or dom m = {} ) & m `2 is Function of (dom m),(cod m) ) by A1, A2, A3, Lm1; :: thesis: verum