Theorem riotaeqi 36655

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

Hypothesis

Ref	Expression
riotaeqi.1	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
riotaeqi	⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥 ∈ 𝐵 𝜑)

Proof of Theorem riotaeqi

Step	Hyp	Ref	Expression
1		riotaeqi.1	. 2 ⊢ 𝐴 = 𝐵
2		biid 264	. 2 ⊢ (𝜑 ↔ 𝜑)
3	1, 2	riotaeqbii 36654	1 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥 ∈ 𝐵 𝜑)

Syntax hints:   = wceq 1568  ℩crio 7366

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1571  df-ex 1808  df-sb 2095  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3455  df-ss 3921  df-uni 4872  df-iota 6492  df-riota 7367

This theorem is referenced by: (None)