Theorem subsub23i

Description: Swap subtrahend and result of subtraction. (Contributed by NM, 7-Oct-1999)

	Ref	Expression
Hypotheses	negidi.1	$$⊢A\in ℂ$$
	pncan3i.2	$$⊢B\in ℂ$$
	subadd.3	$$⊢C\in ℂ$$
Assertion	subsub23i	$$⊢A-B=C\leftrightarrow A-C=B$$

Proof

Step	Hyp	Ref	Expression
1		negidi.1	$$⊢A\in ℂ$$
2		pncan3i.2	$$⊢B\in ℂ$$
3		subadd.3	$$⊢C\in ℂ$$
4		subsub23	$$⊢\left(A\in ℂ\wedge B\in ℂ\wedge C\in ℂ\right)\to \left(A-B=C\leftrightarrow A-C=B\right)$$
5	1 2 3 4	mp3an	$$⊢A-B=C\leftrightarrow A-C=B$$