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Theorem nfiota 5555
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 1609 . . 3  |-  F/ y T.
2 nfiota.1 . . . 4  |-  F/ x ph
32a1i 11 . . 3  |-  ( T. 
->  F/ x ph )
41, 3nfiotad 5554 . 2  |-  ( T. 
->  F/_ x ( iota y ph ) )
54trud 1388 1  |-  F/_ x
( iota y ph )
Colors of variables: wff setvar class
Syntax hints:   T. wtru 1380   F/wnf 1599   F/_wnfc 2615   iotacio 5549
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-rex 2820  df-sn 4028  df-uni 4246  df-iota 5551
This theorem is referenced by:  csbiota  5580  csbiotagOLD  5581  nffv  5873  nfsum1  13478  nfsum  13479  nfcprod1  28895  nfcprod  28896
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