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Theorem cbviotavw 6291
 Description: Change bound variables in a description binder. Version of cbviotav 6293 with a disjoint variable condition, which does not require ax-13 2379. (Contributed by Andrew Salmon, 1-Aug-2011.) (Revised by Gino Giotto, 26-Jan-2024.)
Hypothesis
Ref Expression
cbviotavw.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
cbviotavw (℩𝑥𝜑) = (℩𝑦𝜓)
Distinct variable groups:   𝜑,𝑦   𝜓,𝑥   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑦)

Proof of Theorem cbviotavw
StepHypRef Expression
1 cbviotavw.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
2 nfv 1915 . 2 𝑦𝜑
3 nfv 1915 . 2 𝑥𝜓
41, 2, 3cbviotaw 6290 1 (℩𝑥𝜑) = (℩𝑦𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 209   = wceq 1538  ℩cio 6281 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-in 3888  df-ss 3898  df-sn 4526  df-uni 4801  df-iota 6283 This theorem is referenced by:  oeeui  8213  ellimciota  42271  fourierdlem96  42859  fourierdlem97  42860  fourierdlem98  42861  fourierdlem99  42862  fourierdlem105  42868  fourierdlem106  42869  fourierdlem108  42871  fourierdlem110  42873  fourierdlem112  42875  fourierdlem113  42876  fourierdlem115  42878  funressndmafv2rn  43794
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