Theorem div2subd

Description: Swap subtrahend and minuend inside the numerator and denominator of a fraction. Deduction form of div2sub . (Contributed by David Moews, 28-Feb-2017)

	Ref	Expression
Hypotheses	div2subd.1	$$⊢\phi \to A\in ℂ$$
	div2subd.2	$$⊢\phi \to B\in ℂ$$
	div2subd.3	$$⊢\phi \to C\in ℂ$$
	div2subd.4	$$⊢\phi \to D\in ℂ$$
	div2subd.5	$$⊢\phi \to C\ne D$$
Assertion	div2subd	$$⊢\phi \to \frac{A-B}{C-D}=\frac{B-A}{D-C}$$

Proof

Step	Hyp	Ref	Expression
1		div2subd.1	$$⊢\phi \to A\in ℂ$$
2		div2subd.2	$$⊢\phi \to B\in ℂ$$
3		div2subd.3	$$⊢\phi \to C\in ℂ$$
4		div2subd.4	$$⊢\phi \to D\in ℂ$$
5		div2subd.5	$$⊢\phi \to C\ne D$$
6		div2sub	$$⊢\left(\left(A\in ℂ\wedge B\in ℂ\right)\wedge \left(C\in ℂ\wedge D\in ℂ\wedge C\ne D\right)\right)\to \frac{A-B}{C-D}=\frac{B-A}{D-C}$$
7	1 2 3 4 5 6	syl23anc	$$⊢\phi \to \frac{A-B}{C-D}=\frac{B-A}{D-C}$$