Theorem supex

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

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

Proof

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