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Theorem nfiota1 5412
Description: Bound-variable hypothesis builder for the  iota class. (Contributed by Andrew Salmon, 11-Jul-2011.) (Revised by Mario Carneiro, 15-Oct-2016.)
Assertion
Ref Expression
nfiota1  |-  F/_ x
( iota x ph )

Proof of Theorem nfiota1
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 dfiota2 5411 . 2  |-  ( iota
x ph )  =  U. { y  |  A. x ( ph  <->  x  =  y ) }
2 nfaba1 2576 . . 3  |-  F/_ x { y  |  A. x ( ph  <->  x  =  y ) }
32nfuni 4013 . 2  |-  F/_ x U. { y  |  A. x ( ph  <->  x  =  y ) }
41, 3nfcxfr 2568 1  |-  F/_ x
( iota x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 177   A.wal 1549   {cab 2421   F/_wnfc 2558   U.cuni 4007   iotacio 5408
This theorem is referenced by:  iota2df  5434  sniota  5437  opabiota  6530  nfriota1  6549  nfriotad  6550  erovlem  6992  bnj1366  29138
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-sn 3812  df-uni 4008  df-iota 5410
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