Theorem addsubassi

Description: Associative-type law for subtraction and addition. (Contributed by NM, 16-Sep-1999)

	Ref	Expression
Hypotheses	negidi.1	|- A e. CC
	pncan3i.2	|- B e. CC
	subadd.3	|- C e. CC
Assertion	addsubassi	|- ( ( A + B ) - C ) = ( A + ( B - C ) )

Proof

Step	Hyp	Ref	Expression
1		negidi.1	|- A e. CC
2		pncan3i.2	|- B e. CC
3		subadd.3	|- C e. CC
4		addsubass	|- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( A + B ) - C ) = ( A + ( B - C ) ) )
5	1 2 3 4	mp3an	|- ( ( A + B ) - C ) = ( A + ( B - C ) )