Theorem supex

Description: A supremum is a set. (Contributed by NM, 22-May-1999)

	Ref	Expression
Hypothesis	supex.1	$$⊢R\mathrm{Or}A$$
Assertion	supex	$$⊢sup\left(B,A,R\right)\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		supex.1	$$⊢R\mathrm{Or}A$$
2		id	$$⊢R\mathrm{Or}A\to R\mathrm{Or}A$$
3	2	supexd	$$⊢R\mathrm{Or}A\to sup\left(B,A,R\right)\in \mathrm{V}$$
4	1 3	ax-mp	$$⊢sup\left(B,A,R\right)\in \mathrm{V}$$