let G1, G2, G3 be non empty associative multMagma ; <*G1,G2,G3*> is associative multMagma-Family of {1,2,3}
reconsider A = <*G1,G2,G3*> as multMagma-Family of {1,2,3} ;
A is associative
hence
<*G1,G2,G3*> is associative multMagma-Family of {1,2,3}
; verum