let G1, G2, G3 be non empty multMagma ; :: thesis: <*G1,G2,G3*> is multMagma-Family of {1,2,3}
dom <*G1,G2,G3*> = {1,2,3} by FINSEQ_1:89, FINSEQ_3:1;
then reconsider A = <*G1,G2,G3*> as ManySortedSet of {1,2,3} by PARTFUN1:def 2, RELAT_1:def 18;
A is multMagma-yielding

proof

let y be set ; :: according to GROUP_7:def 1 :: thesis: ( y in rng A implies y is non empty multMagma )
assume y in rng A ; :: thesis: y is non empty multMagma
then consider x being object such that
A1: x in dom A and
A2: A . x = y by FUNCT_1:def 3;
( x = 1 or x = 2 or x = 3 ) by A1, ENUMSET1:def 1;
hence y is non empty multMagma by A2; :: thesis: verum

end;

hence <*G1,G2,G3*> is multMagma-Family of {1,2,3} ; :: thesis: verum