Theorem subaddrii

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

	Ref	Expression
Hypotheses	negidi.1	$$⊢A\in ℂ$$
	pncan3i.2	$$⊢B\in ℂ$$
	subadd.3	$$⊢C\in ℂ$$
	subaddri.4	$$⊢B+C=A$$
Assertion	subaddrii	$$⊢A-B=C$$

Proof

Step	Hyp	Ref	Expression
1		negidi.1	$$⊢A\in ℂ$$
2		pncan3i.2	$$⊢B\in ℂ$$
3		subadd.3	$$⊢C\in ℂ$$
4		subaddri.4	$$⊢B+C=A$$
5	1 2 3	subaddi	$$⊢A-B=C\leftrightarrow B+C=A$$
6	4 5	mpbir	$$⊢A-B=C$$