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Theorem nfiota 5560
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 1673 . . 3  |-  F/ y T.
2 nfiota.1 . . . 4  |-  F/ x ph
32a1i 11 . . 3  |-  ( T. 
->  F/ x ph )
41, 3nfiotad 5559 . 2  |-  ( T. 
->  F/_ x ( iota y ph ) )
54trud 1446 1  |-  F/_ x
( iota y ph )
Colors of variables: wff setvar class
Syntax hints:   T. wtru 1438   F/wnf 1663   F/_wnfc 2568   iotacio 5554
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ral 2778  df-rex 2779  df-sn 3994  df-uni 4214  df-iota 5556
This theorem is referenced by:  csbiota  5585  nffv  5879  nfsum1  13723  nfsum  13724  nfcprod1  13931  nfcprod  13932
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