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Theorem nfriota1 5784
 Description: The abstraction variable in a restricted iota descriptor isn't free. (Contributed by NM, 12-Oct-2011.) (Revised by Mario Carneiro, 15-Oct-2016.)
Assertion
Ref Expression
nfriota1 𝑥(𝑥𝐴 𝜑)
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem nfriota1
StepHypRef Expression
1 df-riota 5777 . 2 (𝑥𝐴 𝜑) = (℩𝑥(𝑥𝐴𝜑))
2 nfiota1 5136 . 2 𝑥(℩𝑥(𝑥𝐴𝜑))
31, 2nfcxfr 2296 1 𝑥(𝑥𝐴 𝜑)
 Colors of variables: wff set class Syntax hints:   ∧ wa 103   ∈ wcel 2128  Ⅎwnfc 2286  ℩cio 5132  ℩crio 5776 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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rex 2441  df-sn 3566  df-uni 3773  df-iota 5134  df-riota 5777 This theorem is referenced by:  riotaprop  5800  riotass2  5803  riotass  5804  lble  8812  oddpwdclemdvds  12035  oddpwdclemndvds  12036
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