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Theorem nfriota1 5506
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 5499 . 2 (𝑥𝐴 𝜑) = (℩𝑥(𝑥𝐴𝜑))
2 nfiota1 4899 . 2 𝑥(℩𝑥(𝑥𝐴𝜑))
31, 2nfcxfr 2217 1 𝑥(𝑥𝐴 𝜑)
Colors of variables: wff set class
Syntax hints:  wa 102  wcel 1434  wnfc 2207  cio 4895  crio 5498
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-sn 3412  df-uni 3610  df-iota 4897  df-riota 5499
This theorem is referenced by:  riotaprop  5522  riotass2  5525  riotass  5526  lble  8092  oddpwdclemdvds  10692  oddpwdclemndvds  10693
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