Theorem subsub23d

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

	Ref	Expression
Hypotheses	subsub23d.1	$$⊢\phi \to A\in ℂ$$
	subsub23d.2	$$⊢\phi \to B\in ℂ$$
	subsub23d.3	$$⊢\phi \to C\in ℂ$$
Assertion	subsub23d	$$⊢\phi \to \left(A-B=C\leftrightarrow A-C=B\right)$$

Proof

Step	Hyp	Ref	Expression
1		subsub23d.1	$$⊢\phi \to A\in ℂ$$
2		subsub23d.2	$$⊢\phi \to B\in ℂ$$
3		subsub23d.3	$$⊢\phi \to C\in ℂ$$
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	syl3anc	$$⊢\phi \to \left(A-B=C\leftrightarrow A-C=B\right)$$