Theorem add12i

Description: Commutative/associative law that swaps the first two terms in a triple sum. (Contributed by NM, 21-Jan-1997)

	Ref	Expression
Hypotheses	add.1	|- A e. CC
	add.2	|- B e. CC
	add.3	|- C e. CC
Assertion	add12i	|- ( A + ( B + C ) ) = ( B + ( A + C ) )

Proof

Step	Hyp	Ref	Expression
1		add.1	|- A e. CC
2		add.2	|- B e. CC
3		add.3	|- C e. CC
4		add12	|- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( A + ( B + C ) ) = ( B + ( A + C ) ) )
5	1 2 3 4	mp3an	|- ( A + ( B + C ) ) = ( B + ( A + C ) )