Theorem subsub23i

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

	Ref	Expression
Hypotheses	negidi.1	|- A e. CC
	pncan3i.2	|- B e. CC
	subadd.3	|- C e. CC
Assertion	subsub23i	|- ( ( A - B ) = C <-> ( A - C ) = B )

Proof

Step	Hyp	Ref	Expression
1		negidi.1	|- A e. CC
2		pncan3i.2	|- B e. CC
3		subadd.3	|- C e. CC
4		subsub23	|- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( A - B ) = C <-> ( A - C ) = B ) )
5	1 2 3 4	mp3an	|- ( ( A - B ) = C <-> ( A - C ) = B )