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

proof

let x be Element of {1,2}; :: according to GROUP_7:def 7 :: thesis: A . x is associative
( x = 1 or x = 2 ) by TARSKI:def 2;
hence A . x is associative ; :: thesis: verum

end;

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