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Theorem cbvriotav 5741
 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 1508 . 2 𝑦𝜑
2 nfv 1508 . 2 𝑥𝜓
3 cbvriotav.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
41, 2, 3cbvriota 5740 1 (𝑥𝐴 𝜑) = (𝑦𝐴 𝜓)
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 104   = wceq 1331  ℩crio 5729 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-sn 3533  df-uni 3737  df-iota 5088  df-riota 5730 This theorem is referenced by:  axcaucvg  7720
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