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Theorem nfiota1 5494
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 5493 . 2  |-  ( iota
x ph )  =  U. { y  |  A. x ( ph  <->  x  =  y ) }
2 nfaba1 2621 . . 3  |-  F/_ x { y  |  A. x ( ph  <->  x  =  y ) }
32nfuni 4208 . 2  |-  F/_ x U. { y  |  A. x ( ph  <->  x  =  y ) }
41, 3nfcxfr 2614 1  |-  F/_ x
( iota x ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184   A.wal 1368   {cab 2439   F/_wnfc 2602   U.cuni 4202   iotacio 5490
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ral 2804  df-rex 2805  df-sn 3989  df-uni 4203  df-iota 5492
This theorem is referenced by:  iota2df  5516  sniota  5519  opabiota  5866  nfriota1  6171  nfriotad  6172  erovlem  7309  bnj1366  32175
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