Theorem riotaeqi 36440

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 263	. 2 ⊢ (𝜑 ↔ 𝜑)
3	1, 2	riotaeqbii 36439	1 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥 ∈ 𝐵 𝜑)

Syntax hints:   = wceq 1548  ℩crio 7315

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1975  ax-7 2016  ax-8 2123  ax-9 2131  ax-ext 2713

This theorem depends on definitions:  df-bi 209  df-an 398  df-tru 1551  df-ex 1788  df-sb 2075  df-clab 2720  df-cleq 2733  df-clel 2816  df-v 3435  df-ss 3901  df-uni 4841  df-iota 6444  df-riota 7316

This theorem is referenced by: (None)