Theorem riotaeqi 37030

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 37029	1 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥 ∈ 𝐵 𝜑)

This proof depends on syntax axioms:   = wceq 1569  ℩crio 7376

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-uni 4867  df-iota 6494  df-riota 7377

This theorem is used by: (None)