Theorem relprcnfsupp

Description: A proper class is never finitely supported. (Contributed by AV, 7-Jun-2019)

	Ref	Expression
Assertion	relprcnfsupp	$$⊢\neg A\in \mathrm{V}\to \neg {finSupp}_Z\left(A\right)$$

Proof

Step	Hyp	Ref	Expression
1		relfsupp	$$⊢\mathrm{Rel}\mathrm{finSupp}$$
2	1	brrelex1i	$$⊢{finSupp}_Z\left(A\right)\to A\in \mathrm{V}$$
3	2	con3i	$$⊢\neg A\in \mathrm{V}\to \neg {finSupp}_Z\left(A\right)$$