let G1, G2 be non empty commutative multMagma ; :: thesis: <*G1,G2*> is commutative multMagma-Family of {1,2}

reconsider A = <*G1,G2*> as multMagma-Family of {1,2} ;

A is commutative

reconsider A = <*G1,G2*> as multMagma-Family of {1,2} ;

A is commutative

proof

hence
<*G1,G2*> is commutative multMagma-Family of {1,2}
; :: thesis: verum
let x be Element of {1,2}; :: according to GROUP_7:def 8 :: thesis: A . x is commutative

( x = 1 or x = 2 ) by TARSKI:def 2;

hence A . x is commutative by FINSEQ_1:44; :: thesis: verum

end;( x = 1 or x = 2 ) by TARSKI:def 2;

hence A . x is commutative by FINSEQ_1:44; :: thesis: verum