Theorem mulassnni

Description: Associative law for multiplication. (Contributed by metakunt, 25-Apr-2024)

	Ref	Expression
Hypotheses	mulassnni.1	|- A e. NN
	mulassnni.2	|- B e. NN
	mulassnni.3	|- C e. NN
Assertion	mulassnni	|- ( ( A x. B ) x. C ) = ( A x. ( B x. C ) )

Proof

Step	Hyp	Ref	Expression
1		mulassnni.1	|- A e. NN
2		mulassnni.2	|- B e. NN
3		mulassnni.3	|- C e. NN
4	1	nncni	|- A e. CC
5	2	nncni	|- B e. CC
6	3	nncni	|- C e. CC
7	4 5 6	mulassi	|- ( ( A x. B ) x. C ) = ( A x. ( B x. C ) )