Theorem oldmaded

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

	Ref	Expression
Hypothesis	oldmaded.1	⊢ ( 𝜑 → 𝐴 ∈ ( O ‘ 𝐵 ) )
Assertion	oldmaded	⊢ ( 𝜑 → 𝐴 ∈ ( M ‘ 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		oldmaded.1	⊢ ( 𝜑 → 𝐴 ∈ ( O ‘ 𝐵 ) )
2		oldssmade	⊢ ( O ‘ 𝐵 ) ⊆ ( M ‘ 𝐵 )
3	2 1	sselid	⊢ ( 𝜑 → 𝐴 ∈ ( M ‘ 𝐵 ) )