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Theorem cbvriotav 6662
Description: Change bound variable in a restricted description binder. (Contributed by NM, 18-Mar-2013.) (Revised by Mario Carneiro, 15-Oct-2016.)
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 1883 . 2 𝑦𝜑
2 nfv 1883 . 2 𝑥𝜓
3 cbvriotav.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
41, 2, 3cbvriota 6661 1 (𝑥𝐴 𝜑) = (𝑦𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196   = wceq 1523  crio 6650
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-rex 2947  df-sn 4211  df-uni 4469  df-iota 5889  df-riota 6651
This theorem is referenced by:  ordtypecbv  8463  fin23lem27  9188  zorn2g  9363  uspgredg2v  26161  usgredg2v  26164  cnlnadji  29063  nmopadjlei  29075  cvmliftlem15  31406  cvmliftiota  31409  cvmlift2  31424  cvmlift3lem7  31433  cvmlift3  31436  lshpkrlem3  34717  cdleme40v  36074  lcfl7N  37107  lcf1o  37157  lcfrlem39  37187  hdmap1cbv  37409  wessf1ornlem  39685  fourierdlem103  40744  fourierdlem104  40745
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