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Theorem nfriota1 5691
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 5684 . 2 (𝑥𝐴 𝜑) = (℩𝑥(𝑥𝐴𝜑))
2 nfiota1 5048 . 2 𝑥(℩𝑥(𝑥𝐴𝜑))
31, 2nfcxfr 2252 1 𝑥(𝑥𝐴 𝜑)
Colors of variables: wff set class
Syntax hints:  wa 103  wcel 1463  wnfc 2242  cio 5044  crio 5683
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2244  df-rex 2396  df-sn 3499  df-uni 3703  df-iota 5046  df-riota 5684
This theorem is referenced by:  riotaprop  5707  riotass2  5710  riotass  5711  lble  8612  oddpwdclemdvds  11690  oddpwdclemndvds  11691
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