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Theorem nfiota 5355
Description: Bound-variable hypothesis builder for the  iota class. (Contributed by NM, 23-Aug-2011.)
Hypothesis
Ref Expression
nfiota.1  |-  F/ x ph
Assertion
Ref Expression
nfiota  |-  F/_ x
( iota y ph )

Proof of Theorem nfiota
StepHypRef Expression
1 nftru 1560 . . 3  |-  F/ y  T.
2 nfiota.1 . . . 4  |-  F/ x ph
32a1i 11 . . 3  |-  (  T. 
->  F/ x ph )
41, 3nfiotad 5354 . 2  |-  (  T. 
->  F/_ x ( iota y ph ) )
54trud 1329 1  |-  F/_ x
( iota y ph )
Colors of variables: wff set class
Syntax hints:    T. wtru 1322   F/wnf 1550   F/_wnfc 2503   iotacio 5349
This theorem is referenced by:  csbiotag  5380  nffv  5668  nfsum1  12404  nfsum  12405  nfcprod1  25008  nfcprod  25009
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ral 2647  df-rex 2648  df-sn 3756  df-uni 3951  df-iota 5351
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