Theorem negsubdid

Description: Distribution of negative over subtraction. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypotheses	negidd.1	$$⊢\phi \to A\in ℂ$$
	pncand.2	$$⊢\phi \to B\in ℂ$$
Assertion	negsubdid	$$⊢\phi \to -\left(A-B\right)=-A+B$$

Proof

Step	Hyp	Ref	Expression
1		negidd.1	$$⊢\phi \to A\in ℂ$$
2		pncand.2	$$⊢\phi \to B\in ℂ$$
3		negsubdi	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to -\left(A-B\right)=-A+B$$
4	1 2 3	syl2anc	$$⊢\phi \to -\left(A-B\right)=-A+B$$