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Theorem cbviotav 6517
Description: Change bound variables in a description binder. Usage of this theorem is discouraged because it depends on ax-13 2366. Use the weaker cbviotavw 6514 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 1910 . 2 𝑦𝜑
3 nfv 1910 . 2 𝑥𝜓
41, 2, 3cbviota 6516 1 (℩𝑥𝜑) = (℩𝑦𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205   = wceq 1534  cio 6504
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2167  ax-13 2366  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1537  df-ex 1775  df-nf 1779  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-v 3464  df-ss 3964  df-sn 4634  df-uni 4914  df-iota 6506
This theorem is referenced by: (None)
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