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Theorem nfiota1 4812
Description: Bound-variable hypothesis builder for the class. (Contributed by Andrew Salmon, 11-Jul-2011.) (Revised by Mario Carneiro, 15-Oct-2016.)
Assertion
Ref Expression
nfiota1 x(℩xφ)

Proof of Theorem nfiota1
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 dfiota2 4811 . 2 (℩xφ) = {yx(φx = y)}
2 nfaba1 2180 . . 3 x{yx(φx = y)}
32nfuni 3577 . 2 x {yx(φx = y)}
41, 3nfcxfr 2172 1 x(℩xφ)
Colors of variables: wff set class
Syntax hints:  wb 98  wal 1240  {cab 2023  wnfc 2162   cuni 3571  cio 4808
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-sn 3373  df-uni 3572  df-iota 4810
This theorem is referenced by:  iota2df  4834  sniota  4837  nfriota1  5418  erovlem  6134
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