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Theorem nfriota1 6844
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 6837 . 2 (𝑥𝐴 𝜑) = (℩𝑥(𝑥𝐴𝜑))
2 nfiota1 6064 . 2 𝑥(℩𝑥(𝑥𝐴𝜑))
31, 2nfcxfr 2937 1 𝑥(𝑥𝐴 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wa 385  wcel 2157  wnfc 2926  cio 6060  crio 6836
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2375  ax-ext 2775
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2784  df-cleq 2790  df-clel 2793  df-nfc 2928  df-ral 3092  df-rex 3093  df-sn 4367  df-uni 4627  df-iota 6062  df-riota 6837
This theorem is referenced by:  riotaprop  6861  riotass2  6864  riotass  6865  riotaxfrd  6868  lble  11265  riotaneg  11292  zriotaneg  11777  nosupbnd1  32364  nosupbnd2  32366  poimirlem26  33915  riotaocN  35221  ltrniotaval  36593  cdlemksv2  36859  cdlemkuv2  36879  cdlemk36  36925  wessf1ornlem  40112  disjinfi  40121
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