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Theorem nfiota1 5221
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 5220 . 2  |-  ( iota
x ph )  =  U. { y  |  A. x ( ph  <->  x  =  y ) }
2 nfaba1 2424 . . 3  |-  F/_ x { y  |  A. x ( ph  <->  x  =  y ) }
32nfuni 3833 . 2  |-  F/_ x U. { y  |  A. x ( ph  <->  x  =  y ) }
41, 3nfcxfr 2416 1  |-  F/_ x
( iota x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   A.wal 1527    = wceq 1623   {cab 2269   F/_wnfc 2406   U.cuni 3827   iotacio 5217
This theorem is referenced by:  iota2df  5243  sniota  5246  opabiota  6293  nfriota1  6312  nfriotad  6313  erovlem  6754  bnj1366  28862
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-sn 3646  df-uni 3828  df-iota 5219
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