Theorem infex

Description: An infimum is a set. (Contributed by AV, 3-Sep-2020)

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

Proof

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