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

Theorem cbviotav 6096
 Description: Change bound variables in a description binder. (Contributed by Andrew Salmon, 1-Aug-2011.)
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 2013 . 2 𝑦𝜑
3 nfv 2013 . 2 𝑥𝜓
41, 2, 3cbviota 6095 1 (℩𝑥𝜑) = (℩𝑦𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 198   = wceq 1656  ℩cio 6088 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-13 2389  ax-ext 2803 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-rex 3123  df-sn 4400  df-uni 4661  df-iota 6090 This theorem is referenced by:  oeeui  7954  ellimciota  40635  fourierdlem96  41207  fourierdlem97  41208  fourierdlem98  41209  fourierdlem99  41210  fourierdlem105  41216  fourierdlem106  41217  fourierdlem108  41219  fourierdlem110  41221  fourierdlem112  41223  fourierdlem113  41224  fourierdlem115  41226  funressndmafv2rn  42119
 Copyright terms: Public domain W3C validator