Theorem riotaeqi

Description: Equal domains yield equal restricted iotas. Inference version. (Contributed by GG, 1-Sep-2025)

	Ref	Expression
Hypothesis	riotaeqi.1	⊢ 𝐴 = 𝐵
Assertion	riotaeqi	⊢ ( ℩ 𝑥 ∈ 𝐴 𝜑 ) = ( ℩ 𝑥 ∈ 𝐵 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		riotaeqi.1	⊢ 𝐴 = 𝐵
2		biid	⊢ ( 𝜑 ↔ 𝜑 )
3	1 2	riotaeqbii	⊢ ( ℩ 𝑥 ∈ 𝐴 𝜑 ) = ( ℩ 𝑥 ∈ 𝐵 𝜑 )