MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  cbviotav Structured version   Visualization version   GIF version

Theorem cbviotav 6303
Description: Change bound variables in a description binder. Usage of this theorem is discouraged because it depends on ax-13 2391. Use the weaker cbviotavw 6301 when possible. (Contributed by Andrew Salmon, 1-Aug-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
cbviotav.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
cbviotav (℩𝑥𝜑) = (℩𝑦𝜓)
Distinct variable groups:   𝜑,𝑦   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑦)

Proof of Theorem cbviotav
StepHypRef Expression
1 cbviotav.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
2 nfv 1915 . 2 𝑦𝜑
3 nfv 1915 . 2 𝑥𝜓
41, 2, 3cbviota 6302 1 (℩𝑥𝜑) = (℩𝑦𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209   = wceq 1538  cio 6291
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 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2178  ax-13 2391  ax-ext 2794
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 2801  df-cleq 2815  df-clel 2894  df-v 3471  df-in 3915  df-ss 3925  df-sn 4540  df-uni 4814  df-iota 6293
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator