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Theorem nfriota1 5399
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(x A φ)
Distinct variable group:   x,A
Allowed substitution hint:   φ(x)

Proof of Theorem nfriota1
StepHypRef Expression
1 df-riota 5393 . 2 (x A φ) = (℩x(x A φ))
2 nfiota1 4796 . 2 x(℩x(x A φ))
31, 2nfcxfr 2157 1 x(x A φ)
Colors of variables: wff set class
Syntax hints:   wa 97   wcel 1374  wnfc 2147  cio 4792  crio 5392
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-rex 2290  df-sn 3356  df-uni 3555  df-iota 4794  df-riota 5393
This theorem is referenced by:  riotaprop  5415  riotass2  5418  riotass  5419
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