Theorem subaddrii

Description: Relationship between subtraction and addition. (Contributed by NM, 16-Dec-2006)

	Ref	Expression
Hypotheses	negidi.1	|- A e. CC
	pncan3i.2	|- B e. CC
	subadd.3	|- C e. CC
	subaddri.4	|- ( B + C ) = A
Assertion	subaddrii	|- ( 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		subaddri.4	|- ( B + C ) = A
5	1 2 3	subaddi	|- ( ( A - B ) = C <-> ( B + C ) = A )
6	4 5	mpbir	|- ( A - B ) = C