Theorem subsub23d

Description: Swap subtrahend and result of subtraction. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypotheses	subsub23d.1	|- ( ph -> A e. CC )
	subsub23d.2	|- ( ph -> B e. CC )
	subsub23d.3	|- ( ph -> C e. CC )
Assertion	subsub23d	|- ( ph -> ( ( A - B ) = C <-> ( A - C ) = B ) )

Proof

Step	Hyp	Ref	Expression
1		subsub23d.1	|- ( ph -> A e. CC )
2		subsub23d.2	|- ( ph -> B e. CC )
3		subsub23d.3	|- ( ph -> 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	syl3anc	|- ( ph -> ( ( A - B ) = C <-> ( A - C ) = B ) )