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Theorem nfiota1 5237
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 5236 . 2  |-  ( iota
x ph )  =  U. { y  |  A. x ( ph  <->  x  =  y ) }
2 nfaba1 2437 . . 3  |-  F/_ x { y  |  A. x ( ph  <->  x  =  y ) }
32nfuni 3849 . 2  |-  F/_ x U. { y  |  A. x ( ph  <->  x  =  y ) }
41, 3nfcxfr 2429 1  |-  F/_ x
( iota x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   A.wal 1530    = wceq 1632   {cab 2282   F/_wnfc 2419   U.cuni 3843   iotacio 5233
This theorem is referenced by:  iota2df  5259  sniota  5262  opabiota  6309  nfriota1  6328  nfriotad  6329  erovlem  6770  bnj1366  29178
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-sn 3659  df-uni 3844  df-iota 5235
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