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Theorem cbviotav 5816
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 1840 . 2 𝑦𝜑
3 nfv 1840 . 2 𝑥𝜓
41, 2, 3cbviota 5815 1 (℩𝑥𝜑) = (℩𝑦𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196   = wceq 1480  cio 5808
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-rex 2913  df-sn 4149  df-uni 4403  df-iota 5810
This theorem is referenced by:  oeeui  7627  ellimciota  39250  fourierdlem96  39726  fourierdlem97  39727  fourierdlem98  39728  fourierdlem99  39729  fourierdlem105  39735  fourierdlem106  39736  fourierdlem108  39738  fourierdlem110  39740  fourierdlem112  39742  fourierdlem113  39743  fourierdlem115  39745
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