Theorem addassnni

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

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

Proof

Step	Hyp	Ref	Expression
1		addassnni.1	|- A e. NN
2		addassnni.2	|- B e. NN
3		addassnni.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	addassi	|- ( ( A + B ) + C ) = ( A + ( B + C ) )