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Theorem nfiota 5414
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 1563 . . 3  |-  F/ y  T.
2 nfiota.1 . . . 4  |-  F/ x ph
32a1i 11 . . 3  |-  (  T. 
->  F/ x ph )
41, 3nfiotad 5413 . 2  |-  (  T. 
->  F/_ x ( iota y ph ) )
54trud 1332 1  |-  F/_ x
( iota y ph )
Colors of variables: wff set class
Syntax hints:    T. wtru 1325   F/wnf 1553   F/_wnfc 2558   iotacio 5408
This theorem is referenced by:  csbiotag  5439  nffv  5727  nfsum1  12476  nfsum  12477  nfcprod1  25228  nfcprod  25229
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-sn 3812  df-uni 4008  df-iota 5410
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