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Theorem nfriota1 7321
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 7314 . 2 (𝑥𝐴 𝜑) = (℩𝑥(𝑥𝐴𝜑))
2 nfiota1 6451 . 2 𝑥(℩𝑥(𝑥𝐴𝜑))
31, 2nfcxfr 2906 1 𝑥(𝑥𝐴 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wa 397  wcel 2107  wnfc 2888  cio 6447  crio 7313
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-nfc 2890  df-ral 3066  df-rex 3075  df-v 3448  df-in 3918  df-ss 3928  df-sn 4588  df-uni 4867  df-iota 6449  df-riota 7314
This theorem is referenced by:  riotaprop  7342  riotass2  7345  riotass  7346  riotaxfrd  7349  ttrcltr  9653  lble  12108  riotaneg  12135  zriotaneg  12617  nosupbnd1  27065  nosupbnd2  27067  noinfbnd1  27080  noinfbnd2  27082  poimirlem26  36107  riotaocN  37674  ltrniotaval  39047  cdlemksv2  39313  cdlemkuv2  39333  cdlemk36  39379  disjinfi  43419
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