Theorem riotaeqi 36178

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 261	. 2 ⊢ (𝜑 ↔ 𝜑)
3	1, 2	riotaeqbii 36177	1 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥 ∈ 𝐵 𝜑)

Syntax hints:   = wceq 1540  ℩crio 7385

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-ss 3967  df-uni 4906  df-iota 6512  df-riota 7386

This theorem is referenced by: (None)