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Theorem cbviotav 5774
 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 1830 . 2 𝑦𝜑
3 nfv 1830 . 2 𝑥𝜓
41, 2, 3cbviota 5773 1 (℩𝑥𝜑) = (℩𝑦𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195   = wceq 1475  ℩cio 5766 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rex 2902  df-sn 4126  df-uni 4373  df-iota 5768 This theorem is referenced by:  oeeui  7569  ellimciota  38681  fourierdlem96  39095  fourierdlem97  39096  fourierdlem98  39097  fourierdlem99  39098  fourierdlem105  39104  fourierdlem106  39105  fourierdlem108  39107  fourierdlem110  39109  fourierdlem112  39111  fourierdlem113  39112  fourierdlem115  39114
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