Theorem fvprcALT

Description: Alternate proof of fvprc using ax-pow instead of ax-sep and ax-pr . (Contributed by NM, 20-May-1998) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		brprcneu	$$⊢\neg A\in \mathrm{V}\to \neg \exists !xAFx$$
2		tz6.12-2	$$⊢\neg \exists !xAFx\to F\left(A\right)=\varnothing$$
3	1 2	syl	$$⊢\neg A\in \mathrm{V}\to F\left(A\right)=\varnothing$$