Theorem afvprc

Description: A function's value at a proper class is the universe, compare with fvprc . (Contributed by Alexander van der Vekens, 25-May-2017)

	Ref	Expression
Assertion	afvprc	$$⊢\neg A\in \mathrm{V}\to \left(F\mathrm{\text{'}\text{'}\text{'}}A\right)=\mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		prcnel	$$⊢\neg A\in \mathrm{V}\to \neg A\in \mathrm{dom}F$$
2		ndmafv	$$⊢\neg A\in \mathrm{dom}F\to \left(F\mathrm{\text{'}\text{'}\text{'}}A\right)=\mathrm{V}$$
3	1 2	syl	$$⊢\neg A\in \mathrm{V}\to \left(F\mathrm{\text{'}\text{'}\text{'}}A\right)=\mathrm{V}$$