Theorem oldmade

Description: An element of an old set is an element of a made set. (Contributed by Scott Fenton, 27-Feb-2026)

	Ref	Expression
Assertion	oldmade	⊢ ( 𝐴 ∈ ( O ‘ 𝐵 ) → 𝐴 ∈ ( M ‘ 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		oldssmade	⊢ ( O ‘ 𝐵 ) ⊆ ( M ‘ 𝐵 )
2	1	sseli	⊢ ( 𝐴 ∈ ( O ‘ 𝐵 ) → 𝐴 ∈ ( M ‘ 𝐵 ) )