Theorem r1fnon

Description: The cumulative hierarchy of sets function is a function on the class of ordinal numbers. (Contributed by NM, 5-Oct-2003) (Revised by Mario Carneiro, 10-Sep-2013)

	Ref	Expression
Assertion	r1fnon	$$⊢R_{1}Fn\mathrm{On}$$

Proof

Step	Hyp	Ref	Expression
1		rdgfnon	$$⊢\mathrm{rec}\left(\left(x\in \mathrm{V}⟼𝒫x\right),\varnothing \right)Fn\mathrm{On}$$
2		df-r1	$$⊢R_1=\mathrm{rec}\left(\left(x\in \mathrm{V}⟼𝒫x\right),\varnothing \right)$$
3	2	fneq1i	$$⊢R_{1}Fn\mathrm{On}\leftrightarrow \mathrm{rec}\left(\left(x\in \mathrm{V}⟼𝒫x\right),\varnothing \right)Fn\mathrm{On}$$
4	1 3	mpbir	$$⊢R_{1}Fn\mathrm{On}$$