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Theorem cbvriotav 7121
Description: Change bound variable in a restricted description binder. Usage of this theorem is discouraged because it depends on ax-13 2392. Use the weaker cbvriotavw 7117 when possible. (Contributed by NM, 18-Mar-2013.) (Revised by Mario Carneiro, 15-Oct-2016.) (New usage is discouraged.)
Hypothesis
Ref Expression
cbvriotav.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
cbvriotav (𝑥𝐴 𝜑) = (𝑦𝐴 𝜓)
Distinct variable groups:   𝑥,𝐴   𝑦,𝐴   𝜑,𝑦   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑦)

Proof of Theorem cbvriotav
StepHypRef Expression
1 nfv 1916 . 2 𝑦𝜑
2 nfv 1916 . 2 𝑥𝜓
3 cbvriotav.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
41, 2, 3cbvriota 7120 1 (𝑥𝐴 𝜑) = (𝑦𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209   = wceq 1538  crio 7106
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 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-13 2392  ax-ext 2796
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 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482  df-in 3926  df-ss 3936  df-sn 4551  df-uni 4825  df-iota 6302  df-riota 7107
This theorem is referenced by: (None)
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