Theorem infex

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

	Ref	Expression
Hypothesis	infex.1	⊢ 𝑅 Or 𝐴
Assertion	infex	⊢ inf ( 𝐵 , 𝐴 , 𝑅 ) ∈ V

Proof

Step	Hyp	Ref	Expression
1		infex.1	⊢ 𝑅 Or 𝐴
2		id	⊢ ( 𝑅 Or 𝐴 → 𝑅 Or 𝐴 )
3	2	infexd	⊢ ( 𝑅 Or 𝐴 → inf ( 𝐵 , 𝐴 , 𝑅 ) ∈ V )
4	1 3	ax-mp	⊢ inf ( 𝐵 , 𝐴 , 𝑅 ) ∈ V